 |
35. All wise men walk on their feet; All unwise men walk on their hands. No man walks on both.
36. No wheelbarrows are comfortable; No uncomfortable vehicles are popular. No wheelbarrows are popular.
37. No frogs are poetical; Some ducks are unpoetical. Some ducks are not frogs.
38. No emperors are dentists; All dentists are dreaded by children. No emperors are dreaded by children.
39. Sugar is sweet; Salt is not sweet. Salt is not sugar.
40. Every eagle can fly; Some pigs cannot fly. Some pigs are not eagles.
Sec. 8. EX8
Sets of Abstract Propositions, proposed as Premisses for Soriteses: Conclusions to be found.
[N.B. At the end of this Section instructions are given for varying these Examples.]
1. 1. No c are d; 2. All a are d; 3. All b are c.
2. 1. All d are b; 2. No a are c'; 3. No b are c.
3. 1. No b are a; 2. No c are d'; 3. All d are b.
4. 1. No b are c; 2. All a are b; 3. No c' are d.
5. 1. All b' are a'; 2. No b are c; 3. No a' are d.
6. 1. All a are b'; 2. No b' are c; 3. All d are a.
7. 1. No d are b'; 2. All b are a; 3. No c are d'.
8. 1. No b' are d; 2. No a' are b; 3. All c are d. pg111 9. 1. All b' are a; 2. No a are d; 3. All b are c.
10. 1. No c are d; 2. All b are c; 3. No a are d'.
11. 1. No b are c; 2. All d are a; 3. All c' are a'.
12. 1. No c are b'; 2. All c' are d'; 3. All b are a.
13. 1. All d are e; 2. All c are a; 3. No b are d'; 4. All e are a'.
14. 1. All e are b; 2. All a are e; 3. All d are b'; 4. All a' are c;
15. 1. No b' are d; 2. All e are c; 3. All b are a; 4. All d' are c'.
16. 1. No a' are e; 2. All d are c'; 3. All a are b; 4. All e' are d.
17. 1. All d are c; 2. All a are e; 3. No b are d'; 4. All c are e'.
18. 1. All a are b; 2. All d are e; 3. All a' are c'; 4. No b are e.
19. 1. No b are c; 2. All e are h; 3. All a are b; 4. No d are h; 5. All e' are c.
20. 1. No d are h'; 2. No c are e; 3. All h are b; 4. No a are d'; 5. No b are e'.
21. 1. All b are a; 2. No d are h; 3. No c are e; 4. No a are h'; 5. All c' are b.
22. 1. All e are d'; 2. No b' are h'; 3. All c' are d; 4. All a are e; 5. No c are h.
23. 1. All b' are a'; 2. No d are e'; 3. All h are b'; 4. No c are e; 5. All d' are a.
24. 1. All h' are k'; 2. No b' are a; 3. All c are d; 4. All e are h'; 5. No d are k'; 6. No b are c'.
25. 1. All a are d; 2. All k are b; 3. All e are h; 4. No a' are b; 5. All d are c; 6. All h are k.
26. 1. All a' are h; 2. No d' are k'; 3. All e are b'; 4. No h are k; 5. All a are e; 6. No b' are d.
27. 1. All c are d'; 2. No h are b; 3. All a' are k; 4. No c are e'; 5. All b' are d; 6. No a are c'.
28. 1. No a' are k; 2. All e are b; 3. No h are k'; 4. No d' are c; 5. No a are b; 6. All c' are h.
29. 1. No e are k; 2. No b' are m; 3. No a are c'; 4. All h' are e; 5. All d are k; 6. No c are b; 7. All d' are l; 8. No h are m'.
30. 1. All n are m; 2. All a' are e; 3. No c' are l; 4. All k are r'; 5. No a are h'; 6. No d are l'; 7. No c are n'; 8. All e are b; 9. All m are r; 10. All h are d.
[N.B. In each Example, in Sections 8 and 9, it is possible to begin with any Premiss, at pleasure, and thus to get as many different Solutions (all of course yielding the same Complete Conclusion) as there are Premisses in the Example. Hence Sec. 8 really contains 129 different Examples, and Sec. 9 contains 273.]
pg112 Sec. 9. EX9
Sets of Concrete Propositions, proposed as Premisses for Soriteses: Conclusions to be found.
1.
(1) Babies are illogical;
(2) Nobody is despised who can manage a crocodile;
(3) Illogical persons are despised.
Univ. "persons"; a = able to manage a crocodile; b = babies; c = despised; d = logical.
2.
(1) My saucepans are the only things I have that are made of tin;
(2) I find all your presents very useful;
(3) None of my saucepans are of the slightest use.
Univ. "things of mine"; a = made of tin; b = my saucepans; c = useful; d = your presents.
3.
(1) No potatoes of mine, that are new, have been boiled;
(2) All my potatoes in this dish are fit to eat;
(3) No unboiled potatoes of mine are fit to eat.
Univ. "my potatoes"; a = boiled; b = eatable; c = in this dish; d = new.
4.
(1) There are no Jews in the kitchen;
(2) No Gentiles say "shpoonj";
(3) My servants are all in the kitchen.
Univ. "persons"; a = in the kitchen; b = Jews; c = my servants; d = saying "shpoonj."
5.
(1) No ducks waltz;
(2) No officers ever decline to waltz;
(3) All my poultry are ducks.
Univ. "creatures"; a = ducks; b = my poultry; c = officers; d = willing to waltz.
6.
(1) Every one who is sane can do Logic;
(2) No lunatics are fit to serve on a jury;
(3) None of your sons can do Logic.
Univ. "persons"; a = able to do Logic; b = fit to serve on a jury; c = sane; d = your sons. pg113 7.
(1) There are no pencils of mine in this box;
(2) No sugar-plums of mine are cigars;
(3) The whole of my property, that is not in this box, consists of cigars.
Univ. "things of mine"; a = cigars; b = in this box; c = pencils; d = sugar-plums.
8.
(1) No experienced person is incompetent;
(2) Jenkins is always blundering;
(3) No competent person is always blundering.
Univ. "persons"; a = always blundering; b = competent; c = experienced; d = Jenkins.
9.
(1) No terriers wander among the signs of the zodiac;
(2) Nothing, that does not wander among the signs of the zodiac, is a comet;
(3) Nothing but a terrier has a curly tail.
Univ. "things"; a = comets; b = curly-tailed; c = terriers; d = wandering among the signs of the zodiac.
10.
(1) No one takes in the Times, unless he is well-educated;
(2) No hedge-hogs can read;
(3) Those who cannot read are not well-educated.
Univ. "creatures"; a = able to read; b = hedge-hogs; c = taking in the Times; d = well-educated.
11.
(1) All puddings are nice;
(2) This dish is a pudding;
(3) No nice things are wholesome.
Univ. "things"; a = nice; b = puddings; c = this dish; d = wholesome.
12.
(1) My gardener is well worth listening to on military subjects;
(2) No one can remember the battle of Waterloo, unless he is very old;
(3) Nobody is really worth listening to on military subjects, unless he can remember the battle of Waterloo.
Univ. "persons"; a = able to remember the battle of Waterloo; b = my gardener; c = well worth listening to on military subjects; d = very old. pg114 13.
(1) All humming-birds are richly coloured;
(2) No large birds live on honey;
(3) Birds that do not live on honey are dull in colour.
Univ. "birds"; a = humming-birds; b = large; c = living on honey; d = richly coloured.
14.
(1) No Gentiles have hooked noses;
(2) A man who is a good hand at a bargain always makes money;
(3) No Jew is ever a bad hand at a bargain.
Univ. "persons"; a = good hands at a bargain; b = hook-nosed; c = Jews; d = making money.
15.
(1) All ducks in this village, that are branded 'B,' belong to Mrs. Bond;
(2) Ducks in this village never wear lace collars, unless they are branded 'B';
(3) Mrs. Bond has no gray ducks in this village.
Univ. "ducks in this village"; a = belonging to Mrs. Bond; b = branded 'B'; c = gray; d = wearing lace-collars.
16.
(1) All the old articles in this cupboard are cracked;
(2) No jug in this cupboard is new;
(3) Nothing in this cupboard, that is cracked, will hold water.
Univ. "things in this cupboard"; a = able to hold water; b = cracked; c = jugs; d = old.
17.
(1) All unripe fruit is unwholesome;
(2) All these apples are wholesome;
(3) No fruit, grown in the shade, is ripe.
Univ. "fruit"; a = grown in the shade; b = ripe; c = these apples; d = wholesome.
18.
(1) Puppies, that will not lie still, are always grateful for the loan of a skipping-rope;
(2) A lame puppy would not say "thank you" if you offered to lend it a skipping-rope.
(3) None but lame puppies ever care to do worsted-work.
Univ. "puppies"; a = caring to do worsted-work; b = grateful for the loan of a skipping-rope; c = lame; d = willing to lie still. pg115 19.
(1) No name in this list is unsuitable for the hero of a romance;
(2) Names beginning with a vowel are always melodious;
(3) No name is suitable for the hero of a romance, if it begins with a consonant.
Univ. "names"; a = beginning with a vowel; b = in this list; c = melodious; d = suitable for the hero of a romance.
20.
(1) All members of the House of Commons have perfect self-command;
(2) No M.P., who wears a coronet, should ride in a donkey-race;
(3) All members of the House of Lords wear coronets.
Univ. "M.P.'s"; a = belonging to the House of Commons; b = having perfect self-command; c = one who may ride in a donkey-race; d = wearing a coronet.
21.
(1) No goods in this shop, that have been bought and paid for, are still on sale;
(2) None of the goods may be carried away, unless labeled "sold";
(3) None of the goods are labeled "sold," unless they have been bought and paid for.
Univ. "goods in this shop"; a = allowed to be carried away; b = bought and paid for; c = labeled "sold"; d = on sale.
22.
(1) No acrobatic feats, that are not announced in the bills of a circus, are ever attempted there;
(2) No acrobatic feat is possible, if it involves turning a quadruple somersault;
(3) No impossible acrobatic feat is ever announced in a circus bill.
Univ. "acrobatic feats"; a = announced in the bills of a circus; b = attempted in a circus; c = involving the turning of a quadruple somersault; d = possible.
23.
(1) Nobody, who really appreciates Beethoven, fails to keep silence while the Moonlight-Sonata is being played;
(2) Guinea-pigs are hopelessly ignorant of music;
(3) No one, who is hopelessly ignorant of music, ever keeps silence while the Moonlight-Sonata is being played.
Univ. "creatures"; a = guinea-pigs; b = hopelessly ignorant of music; c = keeping silence while the Moonlight-Sonata is being played; d = really appreciating Beethoven. pg116 24.
(1) Coloured flowers are always scented;
(2) I dislike flowers that are not grown in the open air;
(3) No flowers grown in the open air are colourless.
Univ. "flowers"; a = coloured; b = grown in the open air; c = liked by me; d = scented.
25.
(1) Showy talkers think too much of themselves;
(2) No really well-informed people are bad company;
(3) People who think too much of themselves are not good company.
Univ. "persons"; a = good company; b = really well-informed; c = showy talkers; d = thinking too much of one's self.
26.
(1) No boys under 12 are admitted to this school as boarders;
(2) All the industrious boys have red hair;
(3) None of the day-boys learn Greek;
(4) None but those under 12 are idle.
Univ. "boys in this school"; a = boarders; b = industrious; c = learning Greek; d = red-haired; e = under 12.
27.
(1) The only articles of food, that my doctor allows me, are such as are not very rich;
(2) Nothing that agrees with me is unsuitable for supper;
(3) Wedding-cake is always very rich;
(4) My doctor allows me all articles of food that are suitable for supper.
Univ. "articles of food"; a = agreeing with me; b = allowed by my doctor; c = suitable for supper; d = very rich; e = wedding-cake.
28.
(1) No discussions in our Debating-Club are likely to rouse the British Lion, so long as they are checked when they become too noisy;
(2) Discussions, unwisely conducted, endanger the peacefulness of our Debating-Club;
(3) Discussions, that go on while Tomkins is in the Chair, are likely to rouse the British Lion;
(4) Discussions in our Debating-Club, when wisely conducted, are always checked when they become too noisy.
Univ. "discussions in our Debating-Club"; a = checked when too noisy; b = dangerous to the peacefulness of our Debating-Club; c = going on while Tomkins is in the chair; d = likely to rouse the British Lion; e = wisely conducted. pg117 29.
(1) All my sons are slim;
(2) No child of mine is healthy who takes no exercise;
(3) All gluttons, who are children of mine, are fat;
(4) No daughter of mine takes any exercise.
Univ. "my children"; a = fat; b = gluttons; c = healthy; d = sons; e = taking exercise.
30.
(1) Things sold in the street are of no great value;
(2) Nothing but rubbish can be had for a song;
(3) Eggs of the Great Auk are very valuable;
(4) It is only what is sold in the street that is really rubbish.
Univ. "things"; a = able to be had for a song; b = eggs of the Great Auk; c = rubbish; d = sold in the street; e = very valuable.
31.
(1) No books sold here have gilt edges, except what are in the front shop;
(2) All the authorised editions have red labels;
(3) All the books with red labels are priced at 5s. and upwards;
(4) None but authorised editions are ever placed in the front shop.
Univ. "books sold here"; a = authorised editions; b = gilt-edged; c = having red labels; d = in the front shop; e = priced at 5s. and upwards.
32.
(1) Remedies for bleeding, which fail to check it, are a mockery;
(2) Tincture of Calendula is not to be despised;
(3) Remedies, which will check the bleeding when you cut your finger, are useful;
(4) All mock remedies for bleeding are despicable.
Univ. "remedies for bleeding"; a = able to check bleeding; b = despicable; c = mockeries; d = Tincture of Calendula; e = useful when you cut your finger.
33.
(1) None of the unnoticed things, met with at sea, are mermaids;
(2) Things entered in the log, as met with at sea, are sure to be worth remembering;
(3) I have never met with anything worth remembering, when on a voyage;
(4) Things met with at sea, that are noticed, are sure to be recorded in the log;
Univ. "things met with at sea"; a = entered in log; b = mermaids; c = met with by me; d = noticed; e = worth remembering. pg118 34.
(1) The only books in this library, that I do not recommend for reading, are unhealthy in tone;
(2) The bound books are all well-written;
(3) All the romances are healthy in tone;
(4) I do not recommend you to read any of the unbound books.
Univ. "books in this library"; a = bound; b = healthy in tone; c = recommended by me; d = romances; e = well-written.
35.
(1) No birds, except ostriches, are 9 feet high;
(2) There are no birds in this aviary that belong to any one but me;
(3) No ostrich lives on mince-pies;
(4) I have no birds less than 9 feet high.
Univ. "birds"; a = in this aviary; b = living on mince-pies; c = my; d = 9 feet high; e = ostriches.
36.
(1) A plum-pudding, that is not really solid, is mere porridge;
(2) Every plum-pudding, served at my table, has been boiled in a cloth;
(3) A plum-pudding that is mere porridge is indistinguishable from soup;
(4) No plum-puddings are really solid, except what are served at my table.
Univ. "plum-puddings"; a = boiled in a cloth; b = distinguishable from soup; c = mere porridge; d = really solid; e = served at my table.
37.
(1) No interesting poems are unpopular among people of real taste;
(2) No modern poetry is free from affectation;
(3) All your poems are on the subject of soap-bubbles;
(4) No affected poetry is popular among people of real taste;
(5) No ancient poem is on the subject of soap-bubbles.
Univ. "poems"; a = affected; b = ancient; c = interesting; d = on the subject of soap-bubbles; e = popular among people of real taste; h = written by you.
38.
(1) All the fruit at this Show, that fails to get a prize, is the property of the Committee;
(2) None of my peaches have got prizes;
(3) None of the fruit, sold off in the evening, is unripe;
(4) None of the ripe fruit has been grown in a hot-house;
(5) All fruit, that belongs to the Committee, is sold off in the evening.
Univ. "fruit at this Show"; a = belonging to the Committee; b = getting prizes; c = grown in a hot-house; d = my peaches; e = ripe; h = sold off in the evening. pg119 39.
(1) Promise-breakers are untrustworthy;
(2) Wine-drinkers are very communicative;
(3) A man who keeps his promises is honest;
(4) No teetotalers are pawnbrokers;
(5) One can always trust a very communicative person.
Univ. "persons"; a = honest; b = pawnbrokers; c = promise-breakers; d = trustworthy; e = very communicative; h = wine-drinkers.
40.
(1) No kitten, that loves fish, is unteachable;
(2) No kitten without a tail will play with a gorilla;
(3) Kittens with whiskers always love fish;
(4) No teachable kitten has green eyes;
(5) No kittens have tails unless they have whiskers.
Univ. "kittens"; a = green-eyed; b = loving fish; c = tailed; d = teachable; e = whiskered; h = willing to play with a gorilla.
41.
(1) All the Eton men in this College play cricket;
(2) None but the Scholars dine at the higher table;
(3) None of the cricketers row;
(4) My friends in this College all come from Eton;
(5) All the Scholars are rowing-men.
Univ. "men in this College"; a = cricketers; b = dining at the higher table; c = Etonians; d = my friends; e = rowing-men; h = Scholars.
42.
(1) There is no box of mine here that I dare open;
(2) My writing-desk is made of rose-wood;
(3) All my boxes are painted, except what are here;
(4) There is no box of mine that I dare not open, unless it is full of live scorpions;
(5) All my rose-wood boxes are unpainted.
Univ. "my boxes"; a = boxes that I dare open; b = full of live scorpions; c = here; d = made of rose-wood; e = painted; h = writing-desks.
43.
(1) Gentiles have no objection to pork;
(2) Nobody who admires pigsties ever reads Hogg's poems;
(3) No Mandarin knows Hebrew;
(4) Every one, who does not object to pork, admires pigsties;
(5) No Jew is ignorant of Hebrew.
Univ. "persons"; a = admiring pigsties; b = Jews; c = knowing Hebrew; d = Mandarins; e = objecting to pork; h = reading Hogg's poems. pg120 44.
(1) All writers, who understand human nature, are clever;
(2) No one is a true poet unless he can stir the hearts of men;
(3) Shakespeare wrote "Hamlet";
(4) No writer, who does not understand human nature, can stir the hearts of men;
(5) None but a true poet could have written "Hamlet.";
Univ. "writers"; a = able to stir the hearts of men; b = clever; c = Shakespeare; d = true poets; e = understanding human nature; h = writer of 'Hamlet.'
45.
(1) I despise anything that cannot be used as a bridge;
(2) Everything, that is worth writing an ode to, would be a welcome gift to me;
(3) A rainbow will not bear the weight of a wheel-barrow;
(4) Whatever can be used as a bridge will bear the weight of a wheel-barrow;
(5) I would not take, as a gift, a thing that I despise.
Univ. "things"; a = able to bear the weight of a wheel-barrow; b = acceptable to me; c = despised by me; d = rainbows; e = useful as a bridge; h = worth writing an ode to.
46.
(1) When I work a Logic-example without grumbling, you may be sure it is one that I can understand;
(2) These Soriteses are not arranged in regular order, like the examples I am used to;
(3) No easy example ever make my head ache;
(4) I ca'n't understand examples that are not arranged in regular order, like those I am used to;
(5) I never grumble at an example, unless it gives me a headache.
Univ. "Logic-examples worked by me"; a = arranged in regular order, like the examples I am used to; b = easy; c = grumbled at by me; d = making my head ache; e = these Soriteses; h = understood by me.
47.
(1) Every idea of mine, that cannot be expressed as a Syllogism, is really ridiculous;
(2) None of my ideas about Bath-buns are worth writing down;
(3) No idea of mine, that fails to come true, can be expressed as a Syllogism;
(4) I never have any really ridiculous idea, that I do not at once refer to my solicitor;
(5) My dreams are all about Bath-buns;
(6) I never refer any idea of mine to my solicitor, unless it is worth writing down.
Univ. "my ideas"; a = able to be expressed as a Syllogism; b = about Bath-buns; c = coming true; d = dreams; e = really ridiculous h = referred to my solicitor; k = worth writing down. pg121 48.
(1) None of the pictures here, except the battle-pieces, are valuable;
(2) None of the unframed ones are varnished;
(3) All the battle-pieces are painted in oils;
(4) All those that have been sold are valuable;
(5) All the English ones are varnished;
(6) All those in frames have been sold.
Univ. "the pictures here"; a = battle-pieces; b = English; c = framed; d = oil-paintings; e = sold; h = valuable; k = varnished.
49.
(1) Animals, that do not kick, are always unexcitable;
(2) Donkeys have no horns;
(3) A buffalo can always toss one over a gate;
(4) No animals that kick are easy to swallow;
(5) No hornless animal can toss one over a gate;
(6) All animals are excitable, except buffaloes.
Univ. "animals"; a = able to toss one over a gate; b = buffaloes; c = donkeys; d = easy to swallow; e = excitable; h = horned; k = kicking.
50.
(1) No one, who is going to a party, ever fails to brush his hair;
(2) No one looks fascinating, if he is untidy;
(3) Opium-eaters have no self-command;
(4) Every one, who has brushed his hair, looks fascinating;
(5) No one wears white kid gloves, unless he is going to a party;
(6) A man is always untidy, if he has no self-command.
Univ. "persons"; a = going to a party; b = having brushed one's hair; c = having self-command; d = looking fascinating; e = opium-eaters; h = tidy; k = wearing white kid gloves.
51.
(1) No husband, who is always giving his wife new dresses, can be a cross-grained man;
(2) A methodical husband always comes home for his tea;
(3) No one, who hangs up his hat on the gas-jet, can be a man that is kept in proper order by his wife;
(4) A good husband is always giving his wife new dresses;
(5) No husband can fail to be cross-grained, if his wife does not keep him in proper order;
(6) An unmethodical husband always hangs up his hat on the gas-jet.
Univ. "husbands"; a = always coming home for his tea; b = always giving his wife new dresses; c = cross-grained; d = good; e = hanging up his hat on the gas-jet; h = kept in proper order; k = methodical. pg122 52.
(1) Everything, not absolutely ugly, may be kept in a drawing-room;
(2) Nothing, that is encrusted with salt, is ever quite dry;
(3) Nothing should be kept in a drawing-room, unless it is free from damp;
(4) Bathing-machines are always kept near the sea;
(5) Nothing, that is made of mother-of-pearl, can be absolutely ugly;
(6) Whatever is kept near the sea gets encrusted with salt.
Univ. "things"; a = absolutely ugly; b = bathing-machines; c = encrusted with salt; d = kept near the sea; e = made of mother-of-pearl; h = quite dry; k = things that may be kept in a drawing-room.
53.
(1) I call no day "unlucky," when Robinson is civil to me;
(2) Wednesdays are always cloudy;
(3) When people take umbrellas, the day never turns out fine;
(4) The only days when Robinson is uncivil to me are Wednesdays;
(5) Everybody takes his umbrella with him when it is raining;
(6) My "lucky" days always turn out fine.
Univ. "days"; a = called by me 'lucky'; b = cloudy; c = days when people take umbrellas; d = days when Robinson is civil to me; e = rainy; h = turning out fine; k = Wednesdays.
54.
(1) No shark ever doubts that it is well fitted out;
(2) A fish, that cannot dance a minuet, is contemptible;
(3) No fish is quite certain that it is well fitted out, unless it has three rows of teeth;
(4) All fishes, except sharks, are kind to children;
(5) No heavy fish can dance a minuet;
(6) A fish with three rows of teeth is not to be despised.
Univ. "fishes"; a = able to dance a minuet; b = certain that he is well fitted out; c = contemptible; d = having 3 rows of teeth; e = heavy; h = kind to children; k = sharks.
55.
(1) All the human race, except my footmen, have a certain amount of common-sense;
(2) No one, who lives on barley-sugar, can be anything but a mere baby;
(3) None but a hop-scotch player knows what real happiness is;
(4) No mere baby has a grain of common sense;
(5) No engine-driver ever plays hop-scotch;
(6) No footman of mine is ignorant of what true happiness is.
Univ. "human beings"; a = engine-drivers; b = having common sense; c = hop-scotch players; d = knowing what real happiness is; e = living on barley-sugar; h = mere babies; k = my footmen. pg123 56.
(1) I trust every animal that belongs to me;
(2) Dogs gnaw bones;
(3) I admit no animals into my study, unless they will beg when told to do so;
(4) All the animals in the yard are mine;
(5) I admit every animal, that I trust, into my study;
(6) The only animals, that are really willing to beg when told to do so, are dogs.
Univ. "animals"; a = admitted to my study; b = animals that I trust; c = dogs; d = gnawing bones; e = in the yard; h = my; k = willing to beg when told.
57.
(1) Animals are always mortally offended if I fail to notice them;
(2) The only animals that belong to me are in that field;
(3) No animal can guess a conundrum, unless it has been properly trained in a Board-School;
(4) None of the animals in that field are badgers;
(5) When an animal is mortally offended, it always rushes about wildly and howls;
(6) I never notice any animal, unless it belongs to me;
(7) No animal, that has been properly trained in a Board-School, ever rushes about wildly and howls.
Univ. "animals"; a = able to guess a conundrum; b = badgers; c = in that field; d = mortally offended; e = my; h = noticed by me; k = properly trained in a Board-School; l = rushing about wildly and howling.
58.
(1) I never put a cheque, received by me, on that file, unless I am anxious about it;
(2) All the cheques received by me, that are not marked with a cross, are payable to bearer;
(3) None of them are ever brought back to me, unless they have been dishonoured at the Bank;
(4) All of them, that are marked with a cross, are for amounts of over L100;
(5) All of them, that are not on that file, are marked "not negotiable";
(6) No cheque of yours, received by me, has ever been dishonoured;
(7) I am never anxious about a cheque, received by me, unless it should happen to be brought back to me;
(8) None of the cheques received by me, that are marked "not negotiable," are for amounts of over L100.
Univ. "cheques received by me"; a = brought back to me; b = cheques that I am anxious about; c = honoured; d = marked with a cross; e = marked 'not negotiable'; h = on that file; k = over L100; l = payable to bearer; m = your. pg124 59.
(1) All the dated letters in this room are written on blue paper;
(2) None of them are in black ink, except those that are written in the third person;
(3) I have not filed any of them that I can read;
(4) None of them, that are written on one sheet, are undated;
(5) All of them, that are not crossed, are in black ink;
(6) All of them, written by Brown, begin with "Dear Sir";
(7) All of them, written on blue paper, are filed;
(8) None of them, written on more than one sheet, are crossed;
(9) None of them, that begin with "Dear Sir," are written in the third person.
Univ. "letters in this room"; a = beginning with "Dear Sir"; b = crossed; c = dated; d = filed; e = in black ink; h = in third person; k = letters that I can read; l = on blue paper; m = on one sheet; n = written by Brown.
60.
(1) The only animals in this house are cats;
(2) Every animal is suitable for a pet, that loves to gaze at the moon;
(3) When I detest an animal, I avoid it;
(4) No animals are carnivorous, unless they prowl at night;
(5) No cats fails to kill mice;
(6) No animals ever take to me, except what are in this house;
(7) Kangaroos are not suitable for pets;
(8) None but carnivora kill mice;
(9) I detest animals that do not take to me;
(10) Animals, that prowl at night, always love to gaze at the moon.
Univ. "animals"; a = avoided by me; b = carnivora; c = cats; d = detested by me; e = in this house; h = kangaroos; k = killing mice; l = loving to gaze at the moon; m = prowling at night; n = suitable for pets; r = taking to me.
pg125
CHAPTER II.
ANSWERS.
Answers to Sec. 1. AN1
1. "All" Sign of Quantity. "persons represented by the Name 'I'" (or "I's") Subject. "are" Copula. "persons who have been out for a walk" Predicate.
or, more briefly,
"All 'I's are persons who have been out for a walk".
2. "All 'I's are persons who feel better".
3. "No persons who are not 'John' are persons who have read the letter".
4. "No Members of the Class 'you and I' are old persons".
5. "No fat creatures are creatures that run well".
6. "No not-brave persons are persons deserving of the fair".
7. "No not-pale persons are persons who look poetical".
8. "Some judges are persons who lose their tempers".
9. "All 'I's are persons who do not neglect important business".
10. "All difficult things are things that need attention".
11. "All unwholesome things are things that should be avoided".
12. "All laws passed last week are laws relating to excise".
13. "All logical studies are things that puzzle me".
14. "No persons in the house are Jews".
15. "Some not well-cooked dishes are unwholesome dishes".
16. "All unexciting books are books that make one drowsy".
17. "All men who know what they're about are men who can detect a sharper".
18. "All Members of the Class 'you and I' are persons who know what they're about".
19. "Some bald persons are persons accustomed to wear wigs".
20. "All fully occupied persons are persons who do not talk about their grievances".
21. "No riddles that can be solved are riddles that interest me".
pg126 Answers to Sec. 2. AN2
1 . -. (O) . - -. (O) (O) - - - - . - -. (O) . -.
2 . -. (I) (O) . - -. - - - - . - -. (O) (O) . -.
3 . -. . - -. (O) - - - - (O) (I) . - -. . -.
4 . -. (O) . - -. (I) - - - (I) (O) (O) . - -. (O) . -.
5 . -. (O) (I) . - -. - - - - . - -. (O) (O) . -.
6 . -. . - -. (O) - - - - (O) (O) . - -. (I) . -.
7 . -. (O) (O) . - -. (I) (O) - - - - (O) . - -. (I) . -.
8 . -. . - -. (O) - - - - (O) . - -. (I) . -.
9 . -. . - -. (O) (O) - - - - (O) (I) . - -. . -.
10 . -. (O) . - -. - - - - (O) (O) . - -. (O) . -.
11 . -. . - -. (O) - - - - (O) . - -. (O) (O) . -.
12 . -. (O) . - -. (I) - - (I) - . - -. (O) . -.
13 . -. . - -. (O) - - - - (I) (O) . - -. (O) (O) . -.
14 . -. (I) . - -. (O) - (I) - - (O) . - -. . -.
15 . -. (O) . - -. - (I) - - . - -. (O) (O) . -.
16 . -. (I) . - -. (O) (O) - - - - (O) . - -. . -.
17 . -. (I) (O) . - -. - - - - . - -. (O) . -.
18 . -. (I) . - -. (O) (O) - - - (I) . - -. . -.
19 . -. . - -. (I) - - - - (O) (O) . - -. . -.
20 . -. . - -. (I) - - - - (O) (O) . - -. . -.
21 . -. (O) . - -. - - (I) - . - -. (I) (O) . -.
22 . -. . - -. (O) (O) - - - - (I) . - -. . -.
23 . -. (O) (O) . - -. (O) - - - - (O) . - -. (I) . -.
24 . -. (O) . - -. (I) - - - - (O) (O) . - -. (O) . -. pg127 25 . -. . - -. (I) (O) - - - - (O) . - -. . -.
26 . -. (O) (O) . - -. - - - - . - -. (I) . -.
27 . -. (O) . - -. - - - - (I) . - -. (O) . -.
28 . -. (O) (O) . - -. (O) - - (I) - (O) . - -. . -.
29 . -. . - -. (O) - - - - (O) (O) . - -. . -.
30 . -. . - -. (O) (O) - - - (I) . - -. . -.
31 . -. (I) (O) . - -. - - (I) - . - -. (O) . -.
32 . -. (O) (I) . - -. (O) (O) - - - - (I) . - -. (O) . -.
Answers to Sec. 3. AN3
1. Some xy exist, or some x are y, or some y are x.
2. No information.
3. All y' are x'.
4. No xy exist, &c.
5. All y' are x.
6. All x' are y.
7. All x are y.
8. All x' are y', and all y are x.
9. All x' are y'.
10. All x are y'.
11. No information.
12. Some x'y' exist, &c.
13. Some xy' exist, &c.
14. No xy' exist, &c.
15. Some xy exist, &c.
16. All y are x.
17. All x' are y, and all y' are x.
18. All x are y', and all y are x'.
19. All x are y, and all y' are x'.
20. All y are x'.
Answers to Sec. 4. AN4
1. No x' are y'.
2. Some x' are y'.
3. Some x are y'.
4. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
5. Some x' are y'.
6. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
7. Some x are y'.
8. Some x' are y'.
9. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
10. All x are y, and all y' are x'.
11. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
12. All y are x'.
13. No x' are y.
14. No x' are y'.
15. No x are y.
16. All x are y', and all y are x'. pg128 17. No x are y'.
18. No x are y.
19. Some x are y'.
20. No x are y'.
21. Some y are x'.
22. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
23. Some x are y.
24. All y are x'.
25. Some y are x'.
26. All y are x.
27. All x are y, and all y' are x'.
28. Some y are x'.
29. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
30. Some y are x'.
31. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
32. No x are y'.
33. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
34. Some x are y.
35. All y are x'.
36. Some y are x'.
37. Some x are y'.
38. No x are y.
39. Some x' are y'.
40. All y' are x.
41. All x are y'.
42. No x are y.
Answers to Sec. 5. AN5
1. Somebody who has been out for a walk is feeling better.
2. No one but John knows what the letter is about.
3. You and I like walking.
4. Honesty is sometimes the best policy.
5. Some greyhounds are not fat.
6. Some brave persons get their deserts.
7. Some rich persons are not Esquimaux.
8. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
9. John is ill.
10. Some things, that are not umbrellas, should be left behind on a journey.
11. No music is worth paying for, unless it causes vibration in the air.
12. Some holidays are tiresome.
13. Englishmen are not Frenchmen.
14. No photograph of a lady is satisfactory.
15. No one looks poetical unless he is phlegmatic.
16. Some thin persons are not cheerful.
17. Some judges do not exercise self-control.
18. Pigs are not fed on barley-water.
19. Some black rabbits are not old. pg129 20. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
21. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
22. Some lessons need attention.
23. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
24. No one, who forgets a promise, fails to do mischief.
25. Some greedy creatures cannot fly.
26. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
27. No bride-cakes are things that need not be avoided.
28. John is happy.
29. Some people, who are not gamblers, are not philosophers.
30. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
31. None of my lodgers write poetry.
32. Senna is not nice.
33. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
34. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
35. Logic is unintelligible.
36. Some wild creatures are fat.
37. All wasps are unwelcome.
38. All black rabbits are young.
39. Some hard-boiled things can be cracked.
40. No antelopes fail to delight the eye.
41. All well-fed canaries are cheerful.
42. Some poetry is not producible at will.
43. No country infested by dragons fails to be fascinating.
44. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
45. Some picturesque things are not made of sugar.
46. No children can sit still.
47. Some cats cannot whistle.
48. You are terrible.
49. Some oysters are not amusing.
50. Nobody in the house has a beard a yard long.
51. Some ill-fed canaries are unhappy.
52. My sisters cannot sing.
53. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
54. Some rich things are nice.
55. My cousins are none of them judges, and judges are none of them cousins of mine.
56. Something wearisome is not eagerly wished for.
57. Senna is nasty.
58. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
59. Niggers are not any of them tall.
60. Some obstinate persons are not philosophers.
61. John is happy.
62. Some unwholesome dishes are not present here (i.e. cannot be spoken of as "these").
63. No books suit feverish patients unless they make one drowsy.
64. Some greedy creatures cannot fly.
65. You and I can detect a sharper.
66. Some dreams are not lambs. pg130 67. No lizard needs a hairbrush.
68. Some things, that may escape notice, are not battles.
69. My cousins are not any of them judges.
70. Some hard-boiled things can be cracked.
71. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
72. She is unpopular.
73. Some people, who wear wigs, are not children of yours.
74. No lobsters expect impossibilities.
75. No nightmare is eagerly desired.
76. Some nice things are not plumcakes.
77. Some kinds of jam need not be shunned.
78. All ducks are ungraceful.
79. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
80. No man, who begs in the street, should fail to keep accounts.
81. Some savage creatures are not spiders.
82. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
83. No travelers, who do not carry plenty of small change, fail to lose their luggage.
84. [No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.]
85. Judges are none of them cousins of mine.
86. All my lodgers are sane.
87. Those who are busy are contented, and discontented people are not busy.
88. None of my cousins are judges.
89. No nightingale dislikes sugar.
90. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
91. Some excuses are not clear explanations.
92. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
93. No kind deed need cause scruple.
94. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
95. [No Concl. Fallacy of Like Eliminands not asserted to exist.]
96. No cheats are trustworthy.
97. No clever child of mine is greedy.
98. Some things, that are meant to amuse, are not Acts of Parliament.
99. No tour, that is ever forgotten, is worth writing a book about.
100. No obedient child of mine is contented.
101. Your visit does not annoy me.
Answers to Sec. 6. AN6
1. Conclusion right.
2. No Concl. Fallacy of Like Eliminands not asserted to exist.
3. Concl. right.
4. Concl. right.
5. Concl. right.
6. No Concl. Fallacy of Like Eliminands not asserted to exist.
7. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
8. Concl. right.
9. Concl. right.
10. Concl. right.
11. Concl. right.
12. Concl. right.
13. Concl. right.
14. Concl. right.
15. Concl. right. pg131 16. No Concl. Fallacy of Like Eliminands not asserted to exist.
17. Concl. right.
18. Concl. right.
19. Concl. right.
20. Concl. right.
21. Concl. right.
22. Concl. wrong: the right one is "Some x are y."
23. Concl. right.
24. Concl. right.
25. Concl. right.
26. Concl. right.
27. Concl. right.
28. No Concl. Fallacy of Like Eliminands not asserted to exist.
29. Concl. right.
30. Concl. right.
31. Concl. right.
32. Concl. right.
33. Concl. right.
34. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
35. Concl. right.
36. Concl. right.
37. Concl. right.
38. No Concl. Fallacy of Like Eliminands not asserted to exist.
39. Concl. right.
40. Concl. right.
Answers to Sec. 7. AN7
1. Concl. right.
2. Concl. right.
3. Concl. right.
4. Concl. wrong: right one is "Some epicures are not uncles of mine."
5. Concl. right.
6. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
7. Concl. wrong: right one is "The publication, in which I saw it, tells lies."
8. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
9. Concl. wrong: right one is "Some tedious songs are not his."
10. Concl. right.
11. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
12. Concl. wrong: right one is "Some fierce creatures do not drink coffee."
13. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
14. Concl. right.
15. Concl. wrong: right one is "Some shallow persons are not students."
16. No Concl. Fallacy of Like Eliminands not asserted to exist.
17. Concl. wrong: right one is "Some business, other than railways, is unprofitable."
18. Concl. wrong: right one is "Some vain persons are not Professors."
19. Concl. right.
20. Concl. wrong: right one is "Wasps are not puppies."
21. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
22. No Concl. Same Fallacy.
23. Concl. right.
24. Concl. wrong: right one is "Some chocolate-creams are delicious."
25. No Concl. Fallacy of Like Eliminands not asserted to exist.
26. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
27. Concl. wrong: right one is "Some pillows are not pokers."
28. Concl. right.
29. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
30. No Concl. Fallacy of Like Eliminands not asserted to exist.
31. Concl. right.
32. No Concl. Fallacy of Like Eliminands not asserted to exist.
33. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss. pg132 34. Concl. wrong: right one is "Some dreaded persons are not begged to prolong their visits."
35. Concl. wrong: right one is "No man walks on neither."
36. Concl. right.
37. No Concl. Fallacy of Unlike Eliminands with an Entity-Premiss.
38. Concl. wrong: right one is "Some persons, dreaded by children, are not emperors."
39. Concl. incomplete: the omitted portion is "Sugar is not salt."
40. Concl. right.
Answers to Sec. 8. AN8
1. a{1}b{0} + b{1}a{0}.
2. d{1}a{0}.
3. ac_{0}.
4. a{1}d{0}.
5. cd_{0}.
6. d{1}c{0}.
7. a'c_{0}.
8. c{1}a'{0}.
9. c'd_{0}.
10. b{1}a{0}.
11. d{1}b{0}.
12. a'd_{0}.
13. e{1}b{0}.
14. d{1}e'{0}.
15. e{1}a'{0}.
16. b'c_{0}.
17. a{1}b{0}.
18. d{1}c{0}.
19. a{1}d{0}.
20. ac_{0}.
21. de_{0}.
22. a{1}b'{0}.
23. h{1}c{0}.
24. e{1}a{0}.
25. e{1}c'{0}.
26. e{1}c'{0}.
27. hk'_{0}.
28. e{1}d'{0}.
29. l'a_{0}.
30. k{1}b'{0}.
Answers to Sec. 9. AN9
1. Babies cannot manage crocodiles.
2. Your presents to me are not made of tin.
3. All my potatoes in this dish are old ones.
4. My servants never say "shpoonj."
5. My poultry are not officers.
6. None of your sons are fit to serve on a jury.
7. No pencils of mine are sugar-plums.
8. Jenkins is inexperienced.
9. No comet has a curly tail.
10. No hedge-hog takes in the Times.
11. This dish is unwholesome.
12. My gardener is very old.
13. All humming-birds are small.
14. No one with a hooked nose ever fails to make money.
15. No gray ducks in this village wear lace collars.
16. No jug in this cupboard will hold water.
17. These apples were grown in the sun.
18. Puppies, that will not lie still, never care to do worsted work.
19. No name in this list is unmelodious.
20. No M.P. should ride in a donkey-race, unless he has perfect self-command.
21. No goods in this shop, that are still on sale, may be carried away. pg133 22. No acrobatic feat, which involves turning a quadruple somersault, is ever attempted in a circus.
23. Guinea-pigs never really appreciate Beethoven.
24. No scentless flowers please me.
25. Showy talkers are not really well-informed.
26. None but red-haired boys learn Greek in this school.
27. Wedding-cake always disagrees with me.
28. Discussions, that go on while Tomkins is in the chair, endanger the peacefulness of our Debating-Club.
29. All gluttons, who are children of mine, are unhealthy.
30. An egg of the Great Auk is not to be had for a song.
31. No books sold here have gilt edges, unless they are priced at 5s. and upwards.
32. When you cut your finger, you will find Tincture of Calendula useful.
33. I have never come across a mermaid at sea.
34. All the romances in this library are well-written.
35. No bird in this aviary lives on mince-pies.
36. No plum-pudding, that has not been boiled in a cloth, can be distinguished from soup.
37. All your poems are uninteresting.
38. None of my peaches have been grown in a hot-house.
39. No pawnbroker is dishonest.
40. No kitten with green eyes will play with a gorilla.
41. All my friends dine at the lower table.
42. My writing-desk is full of live scorpions.
43. No Mandarin ever reads Hogg's poems.
44. Shakespeare was clever.
45. Rainbows are not worth writing odes to.
46. These Sorites-examples are difficult.
47. All my dreams come true.
48. All the English pictures here are painted in oils.
49. Donkeys are not easy to swallow.
50. Opium-eaters never wear white kid gloves.
51. A good husband always comes home for his tea.
52. Bathing-machines are never made of mother-of-pearl.
53. Rainy days are always cloudy.
54. No heavy fish is unkind to children.
55. No engine-driver lives on barley-sugar.
56. All the animals in the yard gnaw bones.
57. No badger can guess a conundrum.
58. No cheque of yours, received by me, is payable to order.
59. I cannot read any of Brown's letters.
60. I always avoid a kangaroo.
pg134
CHAPTER III.
SOLUTIONS.
Sec. 1.
Propositions of Relation reduced to normal form.
Solutions for Sec. 1. SL1
1. The Univ. is "persons." The Individual "I" may be regarded as a Class, of persons, whose peculiar Attribute is "represented by the Name 'I'", and may be called the Class of "I's". It is evident that this Class cannot possibly contain more than one Member: hence the Sign of Quantity is "all". The verb "have been" may be replaced by the phrase "are persons who have been". The Proposition may be written thus:—
"All" Sign of Quantity. "I's" Subject. "are" Copula. "persons who have been out for a walk" Predicate.
or, more briefly,
"All I's are persons who have been out for a walk".
2. The Univ. and the Subject are the same as in Ex. 1. The Proposition may be written
"All I's are persons who feel better".
3. Univ. is "persons". The Subject is evidently the Class of persons from which John is excluded; i.e. it is the Class containing all persons who are not "John".
The Sign of Quantity is "no".
The verb "has read" may be replaced by the phrase "are persons who have read".
The Proposition may be written
"No persons who are not 'John' are persons who have read the letter".
4. Univ. is "persons". The Subject is evidently the Class of persons whose only two Members are "you and I".
Hence the Sign of Quantity is "no".
The Proposition may be written
"No Members of the Class 'you and I' are old persons". pg135 5. Univ. is "creatures". The verb "run well" may be replaced by the phrase "are creatures that run well".
The Proposition may be written
"No fat creatures are creatures that run well".
6. Univ. is "persons". The Subject is evidently the Class of persons who are not brave.
The verb "deserve" may be replaced by the phrase "are deserving of".
The Proposition may be written
"No not-brave persons are persons deserving of the fair".
7. Univ. is "persons". The phrase "looks poetical" evidently belongs to the Predicate; and the Subject is the Class, of persons, whose peculiar Attribute is "not-pale".
The Proposition may be written
"No not-pale persons are persons who look poetical".
8. Univ. is "persons".
The Proposition may be written
"Some judges are persons who lose their tempers".
9. Univ. is "persons". The phrase "never neglect" is merely a stronger form of the phrase "am a person who does not neglect".
The Proposition may be written
"All 'I's' are persons who do not neglect important business".
10. Univ. is "things". The phrase "what is difficult" (i.e. "that which is difficult") is equivalent to the phrase "all difficult things".
The Proposition may be written
"All difficult things are things that need attention".
11. Univ. is "things". The phrase "what is unwholesome" may be interpreted as in Ex. 10.
The Proposition may be written
"All unwholesome things are things that should be avoided".
12. Univ. is "laws". The Predicate is evidently a Class whose peculiar Attribute is "relating to excise".
The Proposition may be written
"All laws passed last week are laws relating to excise".
13. Univ. is "things". The Subject is evidently the Class, of studies, whose peculiar Attribute is "logical"; hence the Sign of Quantity is "all".
The Proposition may be written
"All logical studies are things that puzzle me".
14. Univ. is "persons". The Subject is evidently "persons in the house".
The Proposition may be written
"No persons in the house are Jews".
15. Univ. is "dishes". The phrase "if not well-cooked" is equivalent to the Attribute "not well-cooked".
The Proposition may be written
"Some not well-cooked dishes are unwholesome dishes". pg136 16. Univ. is "books". The phrase "make one drowsy" may be replaced by the phrase "are books that make one drowsy".
The Sign of Quantity is evidently "all".
The Proposition may be written
"All unexciting books are books that make one drowsy".
17. Univ. is "men". The Subject is evidently "a man who knows what he's about"; and the word "when" shows that the Proposition is asserted of every such man, i.e. of all such men. The verb "can" may be replaced by "are men who can".
The Proposition may be written
"All men who know what they're about are men who can detect a sharper".
18. The Univ. and the Subject are the same as in Ex. 4.
The Proposition may be written
"All Members of the Class 'you and I' are persons who know what they're about".
19. Univ. is "persons". The verb "wear" may be replaced by the phrase "are accustomed to wear".
The Proposition may be written
"Some bald persons are persons accustomed to wear wigs".
20. Univ. is "persons". The phrase "never talk" is merely a stronger form of "are persons who do not talk".
The Proposition may be written
"All fully occupied persons are persons who do not talk about their grievances".
21. Univ. is "riddles". The phrase "if they can be solved" is equivalent to the Attribute "that can be solved".
The Proposition may be written
"No riddles that can be solved are riddles that interest me".
Sec. 2.
Method of Diagrams.
Solutions for Sec. 4, Nos. 1-12. SL4-A
. -. . -. 1. No m are x'; (O) All m' are y. . - -. - - (O) (I) - - - . -. (O) (O) . - -. .'. No x' are y'. (O) . -. pg137 . -. . -. 2. No m' are x; (O) (O) Some m' are y'. . - -. - - (I) - - - - . -. . - -. .'. Some x are y'. (I) . -.
. -. . -. 3. All m' are x; (O) (I) (I) All m' are y'. . - -. - - - - - - . -. . - -. .'. Some x are y'. (O) (O) . -.
. -. 4. No x' are m'; (O) All y' are m. . - -. - - (I) - There is no Conclusion. . - -. (O) (O) . -.
. -. . -. 5. Some m are x'; No y are m. . - -. - - (O) (I) - - - - . -. (O) (I) . - -. .'. Some x' are y'. . -.
. -. 6. No x' are m; No m are y. . - -. (O) - - - - There is no Conclusion. (O) (O) . - -. . -.
. -. . -. 7. No m are x'; (I) Some y' are m. . - -. - - (I) - - - - . -. (O) (O) . - -. .'. Some x are y'. . -.
. -. . -. 8. All m' are x'; (O) (O) No m' are y. . - -. - - (I) - - - - . -. . - -. .'. Some x' are y'. (O) (I) . -. pg138 . -. 9. Some x' are m'; No m are y'. . - -. (O) - - - - There is no Conclusion. (O) . - -. (I) . -.
. -. . -. 10. All x are m; (O) (O) (I) (O) All y' are m'. . - -. - - (I) (O) (I) - - - - . -. (O) . - -. .'. All x are y; (I) All y' are x'. . -.
. -. 11. No m are x; All y' are m'. . - -. (O) (O) - - - (I) There is no Conclusion. (O) . - -. . -.
. -. . -. 12. No x are m; (O) (O) All y are m. . - -. - - (O) (O) (I) - - - - . -. (I) . - -. .'. All y are x'. (O) . -.
Solutions for Sec. 5, Nos. 1-12. SL5-A
1. I have been out for a walk; I am feeling better.
Univ. is "persons"; m = the Class of I's; x = persons who have been out for a walk; y = persons who are feeling better.
. -. . -. All m are x; (I) All m are y. . - -. - - (I) (O) - - - - . -. (O) (O) . - -. .'. Some x are y. . -.
i.e. Somebody, who has been out for a walk, is feeling better. pg139 2. No one has read the letter but John; No one, who has not read it, knows what it is about.
Univ. is "persons"; m = persons who have read the letter; x = the Class of Johns; y = persons who know what the letter is about.
. -. . -. No x' are m; (O) No m' are y. . - -. - - (O) - - - - . -. (O) (O) . - -. .'. No x' are y. (O) . -.
i.e. No one, but John, knows what the letter is about.
3. Those who are not old like walking; You and I are young.
Univ. is "persons"; m = old; x = persons who like walking; y = you and I.
. -. . -. All m' are x; (I) (I) All y are m'. . - -. - - (O) (O) - - - - . -. (O) . - -. .'. All y are x. (O) (O) . -.
i.e. You and I like walking.
4. Your course is always honest; Your course is always the best policy.
Univ. is "courses"; m = your; x = honest; y = courses which are the best policy.
. -. . -. All m are x; (I) All m are y. . - -. - - (I) (O) - - - - . -. (O) (O) . - -. .'. Some x are y. . -.
i.e. Honesty is sometimes the best policy.
5. No fat creatures run well; Some greyhounds run well.
Univ. is "creatures"; m = creatures that run well; x = fat; y = greyhounds.
. -. . -. No x are m; Some y are m. . - -. - - (O) (O) (I) - - - - . -. (I) . - -. .'. Some y are x'. . -.
i.e. Some greyhounds are not fat. pg140 6. Some, who deserve the fair, get their deserts; None but the brave deserve the fair.
Univ. is "persons"; m = persons who deserve the fair; x = persons who get their deserts; y = brave.
. -. . -. Some m are x; (I) No y' are m. . - -. - - (I) (O) - - - - . -. (O) . - -. .'. Some y are x. . -.
i.e. Some brave persons get their deserts.
7. Some Jews are rich; All Esquimaux are Gentiles.
Univ. is "persons"; m = Jews; x = rich; y = Esquimaux.
. -. . -. Some m are x; (I) All y are m'. . - -. - - (O) (I) (I) - - - . -. (O) . - -. .'. Some x are y'. . -.
i.e. Some rich persons are not Esquimaux.
8. Sugar-plums are sweet; Some sweet things are liked by children.
Univ. is "things"; m = sweet; x = sugar-plums; y = things that are liked by children.
. -. All x are m; (O) (O) Some m are y. . - -. (I) - (I) - - . - -. . -.
There is no Conclusion.
9. John is in the house; Everybody in the house is ill.
Univ. is "persons"; m = persons in the house; x = the Class of Johns; y = ill.
. -. . -. All x are m; (O) (O) (I) (O) All m are y. . - -. - - (I) (O) - - - - . -. (O) . - -. .'. All x are y. . -.
i.e. John is ill. pg141 10. Umbrellas are useful on a journey; What is useless on a journey should be left behind.
Univ. is "things"; m = useful on a journey; x = umbrellas; y = things that should be left behind.
. -. . -. All x are m; (O) (O) All m' are y. . - -. - - (I) (I) - - - - . -. . - -. .'. Some x' are y. (I) (O) . -.
i.e. Some things, that are not umbrellas, should be left behind on a journey.
11. Audible music causes vibration in the air; Inaudible music is not worth paying for.
Univ. is "music"; m = audible; x = music that causes vibration in the air; y = worth paying for.
. -. . -. All m are x; (O) All m' are y'. . - -. - - (I) (O) - - - (I) . -. (O) (O) . - -. .'. No x' are y. (O) . -.
i.e. No music is worth paying for, unless it causes vibration in the air.
12. Some holidays are rainy; Rainy days are tiresome.
Univ. is "days"; m = rainy; x = holidays; y = tiresome.
. -. . -. Some x are m; (I) All m are y. . - -. - - (I) (O) - - - - . -. (O) . - -. .'. Some x are y. . -.
i.e. Some holidays are tiresome.
Solutions for Sec. 6, Nos. 1-10. SL6-A
1.
Some x are m; No m are y'. Some x are y.
. -. . -. (I) . - -. - - (I) (O) - - - - . -. (O) . - -. Hence proposed Conclusion is right. . -. pg142 2.
All x are m; No y are m'. No y are x'.
. -. (O) (O) . - -. (I) - - - - There is no Conclusion. . - -. (O) . -.
3.
Some x are m'; All y' are m. Some x are y.
. -. . -. (I) (O) (I) . - -. - - - - (I) - . -. . - -. Hence proposed Conclusion is right. (O) . -.
4.
All x are m; No y are m. All x are y'.
. -. . -. (O) (O) (O) (I) . - -. - - (O) (I) - - - - . -. (O) . - -. Hence proposed Conclusion is right. . -.
5.
Some m' are x'; No m' are y. Some x' are y'.
. -. . -. (O) . - -. - - (I) - - - - . -. . - -. Hence proposed Conclusion is right. (O) (I) . -.
6.
No x' are m; All y are m'. All y are x.
. -. . - -. (O) (I) - - - There is no Conclusion. (O) (O) . - -. . -. pg143 7.
Some m' are x'; All y' are m'. Some x' are y'.
. -. . - -. (O) - - - (I) There is no Conclusion. (O) . - -. (I) . -.
8.
No m' are x'; All y' are m'. All y' are x.
. -. . -. (I) (I) . - -. - - (O) (O) - - - - . -. (O) . - -. Hence proposed Conclusion is right. (O) (O) . -.
9.
Some m are x'; No m are y. Some x' are y'.
. -. . -. . - -. - - (O) (I) - - - - . -. (O) (I) . - -. Hence proposed Conclusion is right. . -.
10.
All m' are x'; All m are y. Some y are x'.
. -. . -. (O) (O) . - -. - - (I) - - - - . -. . - -. Hence proposed Conclusion is right. (I) (O) . -.
pg144 Solutions for Sec. 7, Nos. 1-6. SL7-A
1.
No doctors are enthusiastic; You are enthusiastic. You are not a doctor.
Univ. "persons"; m = enthusiastic; x = doctors; y = you.
. -. . -. (O) (O) . - -. - - No x are m; (O) (O) (I) All y are m. - - - - . -. All y are x'. (I) . - -. .'. All y are x'. (O) . -.
Hence proposed Conclusion is right.
2.
All dictionaries are useful; Useful books are valuable. Dictionaries are valuable.
Univ. "books"; m = useful; x = dictionaries; y = valuable.
. -. . -. (O) (O) (I) (O) . - -. - - All x are m; (I) (O) All m are y. - - - - . -. All x are y. (O) . - -. .'. All x are y. . -.
Hence proposed Conclusion is right.
3.
No misers are unselfish; None but misers save egg-shells. No unselfish people save egg-shells.
Univ. "people"; m = misers; x = selfish; y = people who save egg-shells.
. -. . -. (O) . - -. - - No m are x'; (O) No m' are y. - - - - . -. No x' are y. (O) (O) . - -. .'. No x' are y. (O) . -.
Hence proposed Conclusion is right. pg145 4.
Some epicures are ungenerous; All my uncles are generous. My uncles are not epicures.
Univ. "persons"; m = generous; x = epicures; y = my uncles.
. -. . -. (O) (I) (I) . - -. - - Some x are m'. All y are m. - (I) - - . -. All y are x'. . - -. .'. Some x are y'. (O) . -.
Hence proposed Conclusion is wrong, the right one being "Some epicures are not uncles of mine."
5.
Gold is heavy; Nothing but gold will silence him. Nothing light will silence him.
Univ. "things"; m = gold; x = heavy; y = able to silence him.
. -. . -. (O) . - -. - - All m are x; (I) (O) No m' are y. - - - - . -. No x' are y. (O) (O) . - -. .'. No x' are y. (O) . -.
Hence proposed Conclusion is right.
6.
Some healthy people are fat; No unhealthy people are strong. Some fat people are not strong.
Univ. "persons"; m = healthy; x = fat; y = strong.
. -. (O) . - -. Some m are x; (I) No m' are y. - - - - There is no Conclusion. Some x are y'. . - -. (O) . -.
pg146 Sec. 3.
Method of Subscripts.
Solutions for Sec. 4. SL4-B
1. mx'{0} + m'{1}y'{0} > x'y'{0} [Fig. I. i.e. "No x' are y'."
2. m'x_{0} + m'y'_{1} > x'y'_{1} [Fig. II. i.e. "Some x' are y'."
3. m'_{1}x'_{0} + m'_{1}y_{0} > xy'_{1} [Fig. III. i.e. "Some x are y'."
4. x'm'_{0} + y'_{1}m'_{0} > nothing. [Fallacy of Like Eliminands not asserted to exist.]
5. mx'_{1} + ym_{0} > x'y'_{1} [Fig. II. i.e. "Some x' are y'."
6. x'm{0} + my{0} > nothing. [Fallacy of Like Eliminands not asserted to exist.]
7. mx'_{0} + y'm_{1} > xy'_{1} [Fig. II. i.e. "Some x are y'."
8. m'{1}x{0} + m'y{0} > x'y'{1} [Fig. III. i.e. "Some x' are y'."
9. x'm'{1} + my{0} > nothing. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
10. x{1}m'{0} + y'{1}m{0} > x{1}y'{0} + y'{1}x{0} [Fig. I (b). i.e. "All x are y, and all y' are x'."
11. mx_{0} + y'_{1}m_{0} > nothing.1 [Fallacy of Like Eliminands not asserted to exist.]
12. xm_{0} + y_{1}m'_{0} > y_{1}x_{0} [Fig. I (a). i.e. "All y are x'."
13. m'{1}x'{0} + ym{0} > x'y{0} [Fig. I. i.e. "No x' are y."
14. m_{1}x'_{0} + m'_{1}y'_{0} > x'y'_{0} [Fig. I. i.e. "No x' are y'."
15. xm_{0} + m'y_{0} > xy_{0} [Fig. I. i.e. "No x are y."
16. x{1}m{0} + y{1}m'{0} > (x{1}y{0} + y{1}x{0}) [Fig. I (b). i.e. "All x are y' and all y are x'."
17. xm{0} + m'{1}y'{0} > xy'{0} [Fig. I. i.e. "No x are y'."
18. xm'_{0} + my_{0} > xy_{0} [Fig. I. i.e. "No x are y."
19. m_{1}x'_{0} + m_{1}y_{0} > xy'_{1} [Fig. III. i.e. "Some x are y'."
20. mx{0} + m'{1}y'{0} > xy'{0} [Fig. I. i.e. "No x are y'."
21. x{1}m'{0} + m'y{1} > x'y{1} [Fig. II. i.e. "Some x' are y."
22. xm_{1} + y_{1}m'_{0} > nothing. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
23. m{1}x'{0} + ym{1} > xy{1} [Fig. II. i.e. "Some x are y."
24. xm_{0} + y_{1}m'_{0} > y_{1}x_{0} [Fig. I (a). i.e. "All y are x'."
25. mx'_{1} + my'_{0} > x'y_{1} [Fig. II. i.e. "Some x' are y."
26. mx'_{0} + y_{1}m'_{0} > y_{1}x'_{0} [Fig. I (a). i.e. "All y are x."
27. x{1}m{0} + y'{1}m'{0} > (x{1}y'{0} + y'{1}x{0}) [Fig. I (b). i.e. "All x are y, and all y' are x'."
28. m{1}x{0} + my{1} > x'y{1} [Fig. II. i.e. "Some x' are y."
29. mx_{0} + y_{1}m_{0} > nothing. [Fallacy of Like Eliminands not asserted to exist.]
30. x{1}m{0} + ym{1} > x'y{1} [Fig. II. i.e. "Some y are x'."
31. x{1}m'{0} + y{1}m'{0} > nothing. [Fallacy of Like Eliminands not asserted to exist.] pg147 32. xm'{0} + m{1}y'{0} > xy'{0} [Fig. I. i.e. "No x are y'."
33. mx{0} + my{0} > nothing. [Fallacy of Like Eliminands not asserted to exist.]
34. mx'_{0} + ym_{1} > xy_{1} [Fig. II. i.e. "Some x are y."
35. mx_{0} + y_{1}m'_{0} > y_{1}x_{0} [Fig. I (a). i.e. "All y are x'."
36. m{1}x{0} + ym{1} > x'y{1} [Fig. II. i.e. "Some x' are y."
37. m{1}x'{0} + ym{0} > xy'{1} [Fig. III. i.e. "Some x are y'."
38. mx_{0} + m'y_{0} > xy_{0} [Fig. I. i.e. "No x are y."
39. mx'_{1} + my_{0} > x'y'_{1} [Fig. II. i.e. "Some x' are y'."
40. x'm_{0} + y'_{1}m'_{0} > y'_{1}x'_{0} [Fig. I (a). i.e. "All y' are x."
41. x_{1}m_{0} + ym'_{0} > x_{1}y_{0} [Fig. I (a). i.e. "All x are y'."
42. m'x_{0} + ym_{0} > xy_{0} [Fig. I. i.e. "No x are y."
Solutions for Sec. 5, Nos. 13-24. SL5-B
13. No Frenchmen like plumpudding; All Englishmen like plumpudding.
Univ. "men"; m = liking plumpudding; x = French; y = English.
xm_{0} + y_{1}m'_{0} > y_{1}x_{0} [Fig. I (a).
i.e. Englishmen are not Frenchmen.
14. No portrait of a lady, that makes her simper or scowl, is satisfactory; No photograph of a lady ever fails to make her simper or scowl.
Univ. "portraits of ladies"; m = making the subject simper or scowl; x = satisfactory; y = photographic.
mx_{0} + ym'_{0} > xy_{0} [Fig. I.
i.e. No photograph of a lady is satisfactory.
15. All pale people are phlegmatic; No one looks poetical unless he is pale.
Univ. "people"; m = pale; x = phlegmatic; y = looking poetical.
m{1}x'{0} + m'y{0} > x'y{0} [Fig. I.
i.e. No one looks poetical unless he is phlegmatic.
16. No old misers are cheerful; Some old misers are thin.
Univ. "persons"; m = old misers; x = cheerful; y = thin.
mx_{0} + my_{1} > x'y_{1} [Fig. II.
i.e. Some thin persons are not cheerful.
17. No one, who exercises self-control, fails to keep his temper; Some judges lose their tempers.
Univ. "persons"; m = keeping their tempers; x = exercising self-control; y = judges.
xm'_{0} + ym'_{1} > x'y_{1} [Fig. II.
i.e. Some judges do not exercise self-control. pg148 18. All pigs are fat; Nothing that is fed on barley-water is fat.
Univ. is "things"; m = fat; x = pigs; y = fed on barley-water.
x_{1}m'_{0} + ym_{0} > x_{1}y_{0} [Fig. I (a).
i.e. Pigs are not fed on barley-water.
19. All rabbits, that are not greedy, are black; No old rabbits are free from greediness.
Univ. is "rabbits"; m = greedy; x = black; y = old.
m'{1}x'{0} + ym'{0} > xy'{1} [Fig. III.
i.e. Some black rabbits are not old.
20. Some pictures are not first attempts; No first attempts are really good.
Univ. is "things"; m = first attempts; x = pictures; y = really good.
xm'{1} + my{0} > nothing.
[Fallacy of Unlike Eliminands with an Entity-Premiss.]
21. I never neglect important business; Your business is unimportant.
Univ. is "business"; m = important; x = neglected by me; y = your.
mx_{0} + y_{1}m_{0} > nothing.
[Fallacy of Like Eliminands not asserted to exist.]
22. Some lessons are difficult; What is difficult needs attention.
Univ. is "things"; m = difficult; x = lessons; y = needing attention.
xm{1} + m{1}y'{0} > xy{1} [Fig. II.
i.e. Some lessons need attention.
23. All clever people are popular; All obliging people are popular.
Univ. is "people"; m = popular; x = clever; y = obliging.
x{1}m'{0} + y{1}m'{0} > nothing.
[Fallacy of Like Eliminands not asserted to exist.]
24. Thoughtless people do mischief; No thoughtful person forgets a promise.
Univ. is "persons"; m = thoughtful; x = mischievous; y = forgetful of promises.
m'{1}x'{0} + my{0} > x'y{0}
i.e. No one, who forgets a promise, fails to do mischief.
Solutions for Sec. 6. SL6-B
1. xm_{1} + my'_{0} > xy_{1} [Fig. II.] Concl. right.
2. x_{1}m'_{0} + ym'_{0} Fallacy of Like Eliminands not asserted to exist.
3. xm'_{1} + y'_{1}m'_{0} > xy_{1} [Fig. II.] Concl. right. pg149 4. x_{1}m'_{0} + ym_{0} > x_{1}y_{0} [Fig. I (a).] Concl. right.
5. m'x'_{1} + m'y_{0} > x'y'_{1} [Fig. II.] "
6. x'm_{0} + y_{1}m_{0} Fallacy of Like Eliminands not asserted to exist.
7. m'x'_{1} + y'_{1}m_{0} Fallacy of Unlike Eliminands with an Entity-Premiss.
8. m'x'_{0} + y'_{1}m_{0} > y'_{1}x'_{0} [Fig. I (a).] Concl. right.
9. mx'_{1} + my_{0} > x'y'_{1} [Fig. II.] "
10. m'_{1}x_{0} + m'_{1}y'_{0} > x'y_{1} [Fig. III.] "
11. x{1}m{0} + ym{1} > x'y{1} [Fig. II.] "
12. xm_{0} + m'y'_{0} > xy'_{0} [Fig. I.] "
13. xm_{0} + y'_{1}m'_{0} > y'_{1}x_{0} [Fig. I (a).] "
14. m'_{1}x_{0} + m'_{1}y'_{0} > x'y_{1} [Fig. III.] "
15. mx'{1} + y{1}m{0} > x'y'{1} [Fig. II.] "
16. x'm_{0} + y'_{1}m_{0} Fallacy of Like Eliminands not asserted to exist.
17. m'x{0} + m'{1}y{0} > x'y'{1} [Fig. III.] Concl. right.
18. x'm_{0} + my_{1} > xy_{1} [Fig. II.] "
19. mx'{1} + m{1}y'{0} > x'y{1} [ " ] "
20. x'm'_{0} + m'y'_{1} > xy'_{1} [ " ] "
21. mx{0} + m{1}y{0} > x'y'{1} [Fig. III.] "
22. x'{1}m'{0} + ym'{1} > xy{1} [Fig. II.] Concl. wrong: the right one is "Some x are y."
23. m{1}x'{0} + m'y'{0} > x'y'{0} [Fig. I.] Concl. right.
24. x{1}m{0} + m'{1}y'{0} > x{1}y'{0} [Fig. I (a).] "
25. xm'{0} + m{1}y'{0} > xy'{0} [Fig. I.] "
26. m{1}x{0} + y{1}m'{0} > y{1}x{0} [Fig. I (a).] "
27. x_{1}m'_{0} + my'_{0} > x_{1}y'_{0} [ " ] "
28. x_{1}m'_{0} + y'm'_{0} Fallacy of Like Eliminands not asserted to exist.
29. x'm_{0} + m'y'_{0} > x'y'_{0} [Fig. I.] Concl. right.
30. x{1}m'{0} + m{1}y{0} > x{1}y{0} [Fig. I (a).] "
31. x'_{1}m_{0} + y'm'_{0} > x'_{1}y'_{0} [ " ] "
32. xm_{0} + y'm'_{0} > xy'_{0} [Fig. I.] "
33. m{1}x{0} + y'{1}m'{0} > y'{1}x{0} [Fig. I (a).] "
34. x_{1}m_{0} + ym'_{1} Fallacy of Unlike Eliminands with an Entity-Premiss.
35. xm{1} + m{1}y'{0} > xy{1} [Fig. II.] Concl. right.
36. m{1}x{0} + y{1}m'{0} > y{1}x{0} [Fig. I (a).] "
37. mx'{0} + m{1}y{0} > xy'{1} [Fig. III.] "
38. xm{0} + my'{0} Fallacy of Like Eliminands not asserted to exist.
39. mx_{0} + my'_{1} > x'y'_{1} [Fig. II.] Concl. right.
40. mx'_{0} + ym_{1} > xy_{1} [Fig. II.] "
pg150 Solutions for Sec. 7. SL7-B
1. No doctors are enthusiastic; You are enthusiastic. You are not a doctor.
Univ. "persons"; m = enthusiastic; x = doctors; y = you.
xm_{0} + y_{1}m'_{0} > y_{1}x_{0} [Fig. I (a).
Conclusion right.
2. Dictionaries are useful; Useful books are valuable. Dictionaries are valuable.
Univ. "books"; m = useful; x = dictionaries; y = valuable.
x{1}m'{0} + m{1}y'{0} > x{1}y'{0} [Fig. I (a).
Conclusion right.
3. No misers are unselfish; None but misers save egg-shells. No unselfish people save egg-shells.
Univ. "people"; m = misers; x = selfish; y = people who save egg-shells.
mx'_{0} + m'y_{0} > x'y_{0} [Fig. I.
Conclusion right.
4. Some epicures are ungenerous; All my uncles are generous. My uncles are not epicures.
Univ. "persons"; m = generous; x = epicures; y = my uncles.
xm'{1} + y{1}m'{0} > xy'{1} [Fig. II.
Conclusion wrong: right one is "Some epicures are not uncles of mine."
5. Gold is heavy; Nothing but gold will silence him. Nothing light will silence him.
Univ. "things"; m = gold; x = heavy; y = able to silence him.
m{1}x'{0} + m'y{0} > x'y{0} [Fig. I.
Conclusion right.
6. Some healthy people are fat; No unhealthy people are strong. Some fat people are not strong.
Univ. "people"; m = healthy; x = fat; y = strong.
mx{1} + m'y{0}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
7. I saw it in a newspaper; All newspapers tell lies. It was a lie.
Univ. "publications"; m = newspapers; x = publications in which I saw it; y = telling lies.
x{1}m'{0} + m{1}y'{0} > x{1}y'{0} [Fig. I (a).
Conclusion wrong: right one is "The publication, in which I saw it, tells lies." pg151 8. Some cravats are not artistic; I admire anything artistic. There are some cravats that I do not admire.
Univ. "things"; m = artistic; x = cravats; y = things that I admire.
xm_{1} + m_{1}y_{0}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
9. His songs never last an hour. A song, that lasts an hour, is tedious. His songs are never tedious.
Univ. "songs"; m = lasting an hour; x = his; y = tedious.
x_{1}m_{0} + m_{1}y'_{0} > x'y_{1} [Fig. III.
Conclusion wrong: right one is "Some tedious songs are not his."
10. Some candles give very little light; Candles are meant to give light. Some things, that are meant to give light, give very little.
Univ. "things"; m = candles; x = giving &c.; y = meant &c.
mx{1} + m{1}y'{0} > xy{1} [Fig. II.
Conclusion right.
11. All, who are anxious to learn, work hard. Some of these boys work hard. Some of these boys are anxious to learn.
Univ. "persons"; m = hard-working; x = anxious to learn; y = these boys.
x_{1}m'_{0} + ym_{1}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
12. All lions are fierce; Some lions do not drink coffee. Some creatures that drink coffee are not fierce.
Univ. "creatures"; m = lions; x = fierce; y = creatures that drink coffee.
m{1}x'{0} + my'{1} > xy'{1} [Fig. II.
Conclusion wrong: right one is "Some fierce creatures do not drink coffee."
13. No misers are generous; Some old men are ungenerous. Some old men are misers.
Univ. "persons"; m = generous; x = misers; y = old men.
xm{0} + ym'{1}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
14. No fossil can be crossed in love; An oyster may be crossed in love. Oysters are not fossils.
Univ. "things"; m = things that can be crossed in love; x = fossils; y = oysters.
xm_{0} + y_{1}m'_{0} > y_{1}x_{0} [Fig. I (a).
Conclusion right. pg152 15. All uneducated people are shallow; Students are all educated. No students are shallow.
Univ. "people"; m = educated; x = shallow; y = students.
m'_{1}x'_{0} + y_{1}m'_{0} > xy'_{1} [Fig. III.
Conclusion wrong: right one is "Some shallow people are not students."
16. All young lambs jump; No young animals are healthy, unless they jump. All young lambs are healthy.
Univ. "young animals"; m = young animals that jump; x = lambs; y = healthy.
x_{1}m'_{0} + m'y_{0}
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
17. Ill-managed business is unprofitable; Railways are never ill-managed. All railways are profitable.
Univ. "business"; m = ill-managed; x = profitable; y = railways.
m_{1}x_{0} + y_{1}m_{0} > x'y'_{1} [Fig. III.
Conclusion wrong: right one is "Some business, other than railways, is profitable."
18. No Professors are ignorant; All ignorant people are vain. No Professors are vain.
Univ. "people"; m = ignorant; x = Professors; y = vain.
xm{0} + m{1}y'{0} > x'y{1} [Fig. III.
Conclusion wrong: right one is "Some vain persons are not Professors."
19. A prudent man shuns hyaenas. No banker is imprudent. No banker fails to shun hyaenas.
Univ. "men"; m = prudent; x = shunning hyaenas; y = bankers.
m{1}x'{0} + ym'{0} > x'y{0} [Fig. I.
Conclusion right.
20. All wasps are unfriendly; No puppies are unfriendly. No puppies are wasps.
Univ. "creatures"; m = friendly; x = wasps; y = puppies.
x_{1}m_{0} + ym'_{0} > x_{1}y_{0} [Fig. I (a).
Conclusion incomplete: complete one is "Wasps are not puppies".
21. No Jews are honest; Some Gentiles are rich. Some rich people are dishonest.
Univ. "persons"; m = Jews; x = honest; y = rich.
mx{0} + m'y{1}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.] pg153 22. No idlers win fame; Some painters are not idle. Some painters win fame.
Univ. "persons"; m = idlers; x = persons who win fame; y = painters.
mx{0} + ym'{1}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
23. No monkeys are soldiers; All monkeys are mischievous. Some mischievous creatures are not soldiers.
Univ. "creatures"; m = monkeys; x = soldiers; y = mischievous.
mx{0} + m{1}y'{0} > x'y{1} [Fig. III.
Conclusion right.
24. All these bonbons are chocolate-creams; All these bonbons are delicious. Chocolate-creams are delicious.
Univ. "food"; m = these bonbons; x = chocolate-creams; y = delicious.
m_{1}x'_{0} + m_{1}y'_{0} > xy_{1} [Fig. III.
Conclusion wrong, being in excess of the right one, which is "Some chocolate-creams are delicious."
25. No muffins are wholesome; All buns are unwholesome. Buns are not muffins.
Univ. "food"; m = wholesome; x = muffins; y = buns.
xm_{0} + y_{1}m_{0}
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
26. Some unauthorised reports are false; All authorised reports are trustworthy. Some false reports are not trustworthy.
Univ. "reports"; m = authorised; x = true; y = trustworthy.
m'x'_{1} + m_{1}y'_{0}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
27. Some pillows are soft; No pokers are soft. Some pokers are not pillows.
Univ. "things"; m = soft; x = pillows; y = pokers.
xm_{1} + ym_{0} > xy'_{1} [Fig. II.
Conclusion wrong: right one is "Some pillows are not pokers."
28. Improbable stories are not easily believed; None of his stories are probable. None of his stories are easily believed.
Univ. "stories"; m = probable; x = easily believed; y = his.
m'{1}x{0} + ym{0} > xy{0} [Fig. I.
Conclusion right. pg154 29. No thieves are honest; Some dishonest people are found out. Some thieves are found out.
Univ. "people"; m = honest; x = thieves; y = found out.
xm{0} + m'y{1}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
30. No muffins are wholesome; All puffy food is unwholesome. All muffins are puffy.
Univ. is "food"; m = wholesome; x = muffins; y = puffy.
xm_{0} + y_{1}m_{0}
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
31. No birds, except peacocks, are proud of their tails; Some birds, that are proud of their tails, cannot sing. Some peacocks cannot sing.
Univ. "birds"; m = proud of their tails; x = peacocks; y = birds that cannot sing.
x'm_{0} + my'_{1} > xy'_{1} [Fig. II.
Conclusion right.
32. Warmth relieves pain; Nothing, that does not relieve pain, is useful in toothache. Warmth is useful in toothache.
Univ. "applications"; m = relieving pain; x = warmth; y = useful in toothache.
x_{1}m'_{0} + m'y_{0}
No Conclusion. [Fallacy of Like Eliminands not asserted to exist.]
33. No bankrupts are rich; Some merchants are not bankrupts. Some merchants are rich.
Univ. "persons"; m = bankrupts; x = rich; y = merchants.
mx{0} + ym'{1}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
34. Bores are dreaded; No bore is ever begged to prolong his visit. No one, who is dreaded, is ever begged to prolong his visit.
Univ. "persons"; m = bores; x = dreaded; y = begged to prolong their visits.
m{1}x'{0} + my{0} > xy'{1} [Fig. III.
Conclusion wrong: the right one is "Some dreaded persons are not begged to prolong their visits."
35. All wise men walk on their feet; All unwise men walk on their hands. No man walks on both.
Univ. "men"; m = wise; x = walking on their feet; y = walking on their hands.
m_{1}x'_{0} + m'_{1}y'_{0} > x'y'_{0} [Fig. I.
Conclusion wrong: right one is "No man walks on neither." pg155 36. No wheelbarrows are comfortable; No uncomfortable vehicles are popular. No wheelbarrows are popular.
Univ. "vehicles"; m = comfortable; x = wheelbarrows; y = popular.
xm_{0} + m'x_{0} > xy_{0} [Fig. I.
Conclusion right.
37. No frogs are poetical; Some ducks are unpoetical. Some ducks are not frogs.
Univ. "creatures"; m = poetical; x = frogs; y = ducks.
xm{0} + ym'{1}
No Conclusion. [Fallacy of Unlike Eliminands with an Entity-Premiss.]
38. No emperors are dentists; All dentists are dreaded by children. No emperors are dreaded by children.
Univ. "persons"; m = dentists; x = emperors; y = dreaded by children.
xm{0} + m{1}y'{0} > x'y{1} [Fig. III.
Conclusion wrong: right one is "Some persons, dreaded by children, are not emperors."
39. Sugar is sweet; Salt is not sweet. Salt is not sugar.
Univ. "things"; m = sweet; x = sugar; y = salt.
x{1}m'{0} + y{1}m{0} > (x{1}y{0} + y{1}x{0}) [Fig. I (b).
Conclusion incomplete: omitted portion is "Sugar is not salt."
40. Every eagle can fly; Some pigs cannot fly. Some pigs are not eagles.
Univ. "creatures"; m = creatures that can fly; x = eagles; y = pigs.
x{1}m'{0} + ym'{1} > x'y{1} [Fig. II.
Conclusion right.
Solutions for Sec. 8. SL8
1 2 3 1. cd_{0} + a_{1}d'_{0} + b_{1}c'_{0};
1 2 3 cd + ad' + bc' > ab_{0} + a_{1} + b_{1} — = =
i.e. > a{1}b{0} + b{1}a{0}
1 2 3 2. d{1}b'{0} + ac'{0} + bc{0};
1 3 2 db' + bc + ac' > da{0} + d{1} i.e. > d{1}a{0} - =- =
1 2 3 3. ba{0} + cd'{0} + d{1}b'{0};
1 3 2 ba + db' + cd' > ac_{0} - -= =
1 2 3 4. bc{0} + a{1}b'{0} + c'd{0};
1 2 3 bc + ab' + c'd > ad_{0} + a_{1} i.e. > a_{1}d_{0} — = = pg156 1 2 3 1 2 3 5. b'_{1}a_{0} + bc_{0} + a'd_{0}; b'a + bc + a'd > cd_{0} - - = =
1 2 3 6. a_{1}b_{0} + b'c_{0} + d_{1}a'_{0};
1 2 3 ab + b'c + da' > cd{0} + d{1} i.e. > d{1}c{0} — = =
1 2 3 1 2 3 7. db'_{0} + b_{1}a'_{0} + cd'_{0}; db' + ba' + cd' > a'c_{0} — = =
1 2 3 8. b'd{0} + a'b{0} + c{1}d'{0};
1 2 3 b'd + a'b + cd' > a'c{0} + c{1} i.e. > c{1}a'{0} - - = =
1 2 3 9. b'_{1}a'_{0} + ad_{0} + b_{1}c'_{0};
1 2 3 b'a' + ad + bc' > dc'_{0} - - = =
1 2 3 10. cd{0} + b{1}c'{0} + ad'{0};
1 2 3 cd + bc' + ad' > ba{0} + b{1} i.e. > b{1}a{0} — = =
1 2 3 11. bc_{0} + d_{1}a'_{0} + c'_{1}a_{0};
1 3 2 bc + c'a + da' > bd{0} + d{1} i.e. > d{1}b{0} - = - =
1 2 3 12. cb'_{0} + c'_{1}d_{0} + b_{1}a'_{0};
1 2 3 cb' + c'd + ba' > da'_{0} — = =
1 2 3 4 13. d_{1}e'_{0} + c_{1}a'_{0} + bd'_{0} + e_{1}a_{0};
1 3 4 2 de' + bd' + ea + ca' > bc{0} + c{1} i.e. > c{1}b{0} — = =- =
1 2 3 4 14. c{1}b'{0} + a{1}e'{0} + d{1}b{0} + a'{1}c'{0};
1 3 4 2 cb' + db + a'c' + ae' > de'{0} + d{1} i.e. > d{1}e'{0} — = - = =
1 2 3 4 15. b'd_{0} + e_{1}c'_{0} + b_{1}a'_{0} + d'_{1}c_{0};
1 3 4 2 b'd + ba' + d'c + ec' > a'e{0} + e{1} i.e. > e{1}a'{0} - - = = - =
1 2 3 4 16. a'e_{0} + d_{1}c_{0} + a_{1}b'_{0} + e'_{1}d'_{0};
1 3 4 2 a'e + ab' + e'd' + dc > b'c_{0} - - = = - =
1 2 3 4 17. d_{1}c'_{0} + a_{1}e'_{0} + bd'_{0} + c_{1}e_{0};
1 3 4 2 dc' + bd' + ce + ae' > ba{0} + a{1} i.e. > a{1}b{0} — = =- =
1 2 3 4 18. a_{1}b'_{0} + d_{1}e'_{0} + a'_{1}c_{0} + be_{0};
1 3 4 2 ab' + a'c + be + de' > cd{0} + d{1} i.e. > d{1}c{0} — = =- =
1 2 3 4 5 19. bc{0} + e{1}h'{0} + a{1}b'{0} + dh{0} + e'{1}c'{0};
1 3 5 2 4 bc + ab' + e'c' + eh' + dh > ad{0} + a{1} — = - = =- =
i.e. > a{1}d{0}
1 2 3 4 5 20. dh'{0} + ce{0} + h{1}b'{0} + ad'{0} + be'{0};
1 3 4 5 2 dh' + hb' + ad' + be' + ce > ac_{0} — =- = =- =
1 2 3 4 5 21. b_{1}a'_{0} + dh_{0} + ce_{0} + ah'_{0} + c'_{1}b'_{0};
1 4 2 5 3 ba' + ah' + dh + c'b' + ce > de_{0} — - = - =
1 2 3 4 5 22. e{1}d{0} + b'h'{0} + c'{1}d'{0} + a{1}e'{0} + ch{0};
1 3 4 5 2 ed + c'd' + ae' + ch + b'h' > ab'{0} + a{1} — - = = =- =
i.e. > a{1}b{0} pg157 1 2 3 4 5 23. b'{1}a{0} + de'{0} + h{1}b{0} + ce{0} + d'{1}a'{0};
1 3 5 2 4 b'a + hb + d'a' + de' + ce - - = - = =- =
> hc{0} + h{1} i.e. > h{1}c{0}
1 2 3 4 5 6 24. h'_{1}k_{0} + b'a_{0} + c_{1}d'_{0} + e_{1}h_{0} + dk'_{0} + bc'_{0};
1 4 5 3 6 2 h'k + eh + dk' + cd' + bc' + b'a > ea{0} + e{1} - - = -= -= -= =
i.e. > e{1}a{0}
1 2 3 4 25. a_{1}d'_{0} + k_{1}b'_{0} + e_{1}h'_{0} + a'b_{0}
5 6 + d{1}c'{0} + h{1}k'{0};
1 4 2 5 6 3 ad' + a'b + kb' + dc' + hk' + eh' > c'e{0} + e{1} — = - -= = -= =
i.e. > e{1}c'{0}
1 2 3 4 5 26. a'_{1}h'_{0} + d'k'_{0} + e_{1}b_{0} + hk_{0} + a_{1}c'_{0} 6 + b'd_{0};
1 4 2 5 6 3 a'h' + hk + d'k' + ac' + b'd + eb > c'e{0} + e{1} - - =- - = = - = =
i.e. > e{1}c'{0}
1 2 3 4 5 27. e{1}d{0} + hb{0} + a'{1}k'{0} + ce'{0} + b'{1}d'{0}
6 + ac'_{0};
1 4 5 2 6 3 ed + ce' + b'd' + hb + ac' + a'k' > hk'_{0} — -= - = = -= =
1 2 3 4 5 28. a'k{0} + e{1}b'{0} + hk'{0} + d'c{0} + ab{0}
6 + c'{1}h'{0};
1 3 5 2 6 4 a'k + hk' + ab + eb' + c'h' + d'c > ed'{0} + e{1} - - -= =- = - = =
i.e. > e{1}d'{0}
1 2 3 4 5 29. ek_{0} + b'm_{0} + ac'_{0} + h'_{1}e'_{0} + d_{1}k'_{0}
6 7 8 + cb{0} + d'{1}l'{0} + hm'{0};
1 4 5 7 8 2 6 3 ek + h'e' + dk' + d'l' + hm' + b'm + cb + ac' — - = - = - - = -= =
> l'a_{0}
1 2 3 4 5 30. n{1}m'{0} + a'{1}e'{0} + c'l{0} + k{1}r{0} + ah'{0}
6 7 8 9 10 + dl'{0} + cn'{0} + e{1}b'{0} + m{1}r'{0} + h{1}d'{0};
1 7 3 6 9 4 10 5 2 8 nm' + cn' + c'l + dl' + mr' + kr + hd' + ah' + a'e' + eb' — - = - - - = - -= = - =
> kb'{0} + k{1} i.e. > k{1}b'{0}
Solutions for Sec. 9. SL9
1.
1 2 3 b_{1}d_{0} + ac_{0} + d'_{1}c'_{0};
1 3 2 bd + d'c' + ac > ba{0} + b{1}, i.e. > b{1}a{0} - = - =
i.e. Babies cannot manage crocodiles.
2.
1 2 3 a_{1}b'_{0} + d_{1}c'_{0} + bc_{0};
1 3 2 ab' + bc + dc' > ad{0} + d{1}, i.e. > d{1}a{0} - =- =
i.e. Your presents to me are not made of tin. pg158 3.
1 2 3 da{0} + c{1}b'{0} + a'b{0};
1 3 2 da + a'b + cb' > dc{0} + c{1}, i.e. > c{1}d{0} - = - =
i.e. All my potatoes in this dish are old ones.
4.
1 2 3 ba{0} + b'd{0} + c{1}a'{0};
1 2 3 ba + b'd + ca' > dc{0} + c{1}, i.e. > c{1}d{0} — = =
i.e. My servants never say "shpoonj."
5.
1 2 3 ad{0} + cd'{0} + b{1}a'{0};
1 2 3 ad + cd' + ba' > cb{0} + b{1}, i.e. > b{1}c{0} — = =
i.e. My poultry are not officers.
6.
1 2 3 1 2 3 c_{1}a'_{0} + c'b_{0} + da_{0}; ca' + c'b + da > bd_{0} — = =
i.e. None of your sons are fit to serve on a jury.
7.
1 2 3 1 3 2 cb_{0} + da_{0} + b'_{1}a'_{0}; cb + b'a' + da > cd_{0} - = - =
i.e. No pencils of mine are sugarplums.
8.
1 2 3 cb'{0} + d{1}a'{0} + ba{0};
1 3 2 cb' + ba + da' > cd{0} + d{1}, i.e. > d{1}c{0} - =- =
i.e. Jenkins is inexperienced.
9.
1 2 3 1 2 3 cd{0} + d'a{0} + c'b{0}; cd + d'a + c'b > ab{0} — = =
i.e. No comet has a curly tail.
10.
1 2 3 1 3 2 d'c_{0} + ba_{0} + a'_{1}d_{0}; d'c + a'd + ba > cb_{0} - - = =
i.e. No hedgehog takes in the Times.
11.
1 2 3 b_{1}a'_{0} + c_{1}b'_{0} + ad_{0};
1 2 3 ba' + cb' + ad > cd{0} + c{1}, i.e. > c{1}d{0} — = =
i.e. This dish is unwholesome.
12.
1 2 3 b{1}c'{0} + d'a{0} + a'c{0};
1 3 2 bc' + a'c + d'a > bd'{0} + b{1}, i.e. > b{1}d'{0} - - = =
i.e. My gardener is very old.
13.
1 2 3 a_{1}d'_{0} + bc_{0} + c'_{1}d_{0};
1 3 2 ad' + c'd + bc > ab{0} + a{1}, i.e. > a{1}b{0} - - = =
i.e. All humming-birds are small. pg159 14.
1 2 3 1 3 2 c'b_{0} + a_{1}d'_{0} + ca'_{0}; c'b + ca' + ad' > bd'_{0} - =- =
i.e. No one with a hooked nose ever fails to make money.
15.
1 2 3 1 2 3 b{1}a'{0} + b'{1}d{0} + ca{0}; ba' + b'd + ca > dc{0} — = =
i.e. No gray ducks in this village wear lace collars.
16.
1 2 3 1 2 3 d_{1}b'_{0} + cd'_{0} + ba_{0}; db' + cd' + ba > ca_{0} — = =
i.e. No jug in this cupboard will hold water.
17.
1 2 3 b'_{1}d_{0} + c_{1}d'_{0} + ab_{0};
1 2 3 b'd + cd' + ab > ca{0} + c{1}, i.e. > c{1}a{0} - - = =
i.e. These apples were grown in the sun.
18.
1 2 3 d'_{1}b'_{0} + c_{1}b_{0} + c'a_{0};
1 2 3 d'b' + cb + c'a > d'a{0} + d'{1}, i.e. > d'{1}a{0} - -= =
i.e. Puppies, that will not lie still, never care to do worsted-work.
19.
1 2 3 1 3 2 bd'_{0} + a_{1}c'_{0} + a'd_{0}; bd' + a'd + ac' > bc'_{0} - - = =
i.e. No name in this list is unmelodious.
20.
1 2 3 1 3 2 a{1}b'{0} + dc{0} + a'{1}d'{0}; ab' + a'd' + dc > b'c{0} - = - =
i.e. No M.P. should ride in a donkey-race, unless he has perfect self-command.
21.
1 2 3 1 3 2 bd{0} + c'a{0} + b'c{0}; bd + b'c + c'a > da{0} - = - =
i.e. No goods in this shop, that are still on sale, may be carried away.
22.
1 2 3 1 3 2 a'b{0} + cd{0} + d'a{0}; a'b + d'a + cd > bc{0} - - = =
i.e. No acrobatic feat, which involves turning a quadruple somersault, is ever attempted in a circus.
23.
1 2 3 dc'{0} + a{1}b'{0} + bc{0};
1 3 2 dc' + bc + ab' > da{0} + a{1}, i.e. > a{1}d{0} - -= =
i.e. Guinea-pigs never really appreciate Beethoven. pg160 24.
1 2 3 1 3 2 a{1}d'{0} + b'{1}c{0} + ba'{0}; ad' + ba' + b'c > d'c{0} - -= =
i.e. No scentless flowers please me.
25.
1 2 3 c_{1}d'_{0} + ba'_{0} + d_{1}a_{0};
1 3 2 cd' + da + ba' > cb{0} + c{1}, i.e. > c{1}b{0} - =- =
i.e. Showy talkers are not really well-informed.
26.
1 2 3 4 ea{0} + b{1}d'{0} + a'{1}c{0} + e'b'{0};
1 3 4 2 ea + a'c + e'b' + bd' > cd'_{0} — = = - =
i.e. None but red-haired boys learn Greek in this school.
27.
1 2 3 4 b_{1}d_{0} + ac'_{0} + e_{1}d'_{0} + c_{1}b'_{0};
1 3 4 2 bd + ed' + cb' + ac' > ea{0} + e{1}, i.e. > e{1}a{0} — = -= =
i.e. Wedding-cake always disagrees with me.
28.
1 2 3 4 ad_{0} + e'_{1}b'_{0} + c_{1}d'_{0} + e_{1}a'_{0};
1 3 4 2 ad + cd' + ea' + e'b' > cb'{0} + c{1}, i.e. > c{1}b'{0} — = -= =
i.e. Discussions, that go on while Tomkins is in the chair, endanger the peacefulness of our Debating-Club.
29.
1 2 3 4 d{1}a{0} + e'c{0} + b{1}a'{0} + d'e{0};
1 3 4 2 da + ba' + d'e + e'c > bc{0} + b{1}, i.e. > b{1}c{0} — = = - =
i.e. All gluttons in my family are unhealthy.
30.
1 2 3 4 d_{1}e_{0} + c'a_{0} + b_{1}e'_{0} + c_{1}d'_{0};
1 3 4 2 de + be' + cd' + c'a > ba{0} + b{1}, i.e. > b{1}a{0} — = -= =
i.e. An egg of the Great Auk is not to be had for a song.
31.
1 2 3 4 d'b{0} + a{1}c'{0} + c{1}e'{0} + a'd{0};
1 4 2 3 d'b + a'd + ac' + ce' > be'_{0} - - = =- =
i.e. No books sold here have gilt edges unless they are priced at 5s. and upwards.
32.
1 2 3 4 a'{1}c'{0} + d{1}b{0} + a{1}e'{0} + c{1}b'{0};
1 3 4 2 a'c' + ae' + cb' + db > e'd{0} + d{1}, i.e. > d{1}e'{0} - - = =- =
i.e. When you cut your finger, you will find Tincture of Calendula useful.
33.
1 2 3 4 d'b{0} + a{1}e'{0} + ec{0} + d{1}a'{0};
1 4 2 3 d'b + da' + ae' + ec > bc_{0} - =- =- =
i.e. I have never come across a mermaid at sea. pg161 34.
1 2 3 4 c'{1}b{0} + a{1}e'{0} + d{1}b'{0} + a'{1}c{0};
1 3 4 2 c'b + db' + a'c + ae' > de'{0} + d{1}, i.e. > d{1}e'{0} - - = - = =
i.e. All the romances in this library are well-written.
35.
1 2 3 4 e'd{0} + c'a{0} + eb{0} + d'c{0};
1 3 4 2 e'd + eb + d'c + c'a > ba_{0} - - = = - =
i.e. No bird in this aviary lives on mince-pies.
36.
1 2 3 4 d'_{1}c'_{0} + e_{1}a'_{0} + c_{1}b_{0} + e'd_{0};
1 3 4 2 d'c' + cb + e'd + ea' > ba'_{0} - - = - = =
i.e. No plum-pudding, that has not been boiled in a cloth, can be distinguished from soup.
37.
1 2 3 4 5 ce'{0} + b'a'{0} + h{1}d'{0} + ae{0} + bd{0};
1 4 2 5 3 ce' + ae + b'a' + bd + hd' > ch{0} + h{1}, i.e. > h{1}c{0} - -= - = =- =
i.e. All your poems are uninteresting.
38.
1 2 3 4 5 b'_{1}a'_{0} + db_{0} + he'_{0} + ec_{0} + a_{1}h'_{0};
1 2 5 3 4 b'a' + db + ah' + he' + ec > dc_{0} - - = =- =- =
i.e. None of my peaches have been grown in a hothouse.
39.
1 2 3 4 5 c_{1}d_{0} + h_{1}e'_{0} + c'_{1}a'_{0} + h'b_{0} + e_{1}d'_{0}; |
|
