20. No m are x;
All m′ are y.
21. All x are m;
Some m′ are y.
22. Some x are m;
All y are m.
23. All m are x;
Some y are m.
24. No x are m;
All y are m.
25. Some m are x′;
All y′ are m′.
26. No m are x′;
All y are m.
27. All x are m′;
All y′ are m.
28. All m are x′;
Some m are y.
29. No m are x;
All y are m′.
30. All x are m′;
Some y are m.
31. All x are m;
All y are m.
32. No x are m′;
All m are y.
33. No m are x;
No m are y.
34. No m are x′;
Some y are m.
35. No m are x;
All y are m.
36. All m are x′;
Some y are m.
37. All m are x;
No y are m.
38. No m are x;
No m′ are y.
39. Some m are x′;
No m are y.
40. No x′ are m;
All y′ are m.
41. All x are m′;
No y are m′.
42. No m′ are x;
No y are m.
EX5§ 5.
Pairs of Concrete Propositions, proposed as Premisses: Conclusions to be found.
1. I have been out for a walk;
I am feeling better.
2. No one has read the letter but John;
No one, who has not read it, knows what it is about.
3. Those who are not old like walking;
You and I are young.
4. Your course is always honest;
Your course is always the best policy.
5. No fat creatures run well;
Some greyhounds run well.
6. Some, who deserve the fair, get their deserts;
None but the brave deserve the fair.
7. Some Jews are rich;
All Esquimaux are Gentiles.
8. Sugar-plums are sweet;
Some sweet things are liked by children.
9. John is in the house;
Everybody in the house is ill.
10. Umbrellas are useful on a journey;
What is useless on a journey should be left behind.
11. Audible music causes vibration in the air;
Inaudible music is not worth paying for.
12. Some holidays are rainy;
Rainy days are tiresome.
13. No Frenchmen like plumpudding;
All Englishmen like plumpudding.
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.
15. All pale people are phlegmatic;
No one looks poetical unless he is pale.
16. No old misers are cheerful;
Some old misers are thin.
17. No one, who exercises self-control, fails to keep his temper;
Some judges lose their tempers.
18. All pigs are fat;
Nothing that is fed on barley-water is fat.
19. All rabbits, that are not greedy, are black;
No old rabbits are free from greediness.
20. Some pictures are not first attempts;
No first attempts are really good.
21. I never neglect important business;
Your business is unimportant.
22. Some lessons are difficult;
What is difficult needs attention.
23. All clever people are popular;
All obliging people are popular.
24. Thoughtless people do mischief;
No thoughtful person forgets a promise.
25. Pigs cannot fly;
Pigs are greedy.
26. All soldiers march well;
Some babies are not soldiers.
27. No bride-cakes are wholesome;
What is unwholesome should be avoided.
28. John is industrious;
No industrious people are unhappy.
29. No philosophers are conceited;
Some conceited persons are not gamblers.
30. Some excise laws are unjust;
All the laws passed last week relate to excise.
31. No military men write poetry;
None of my lodgers are civilians.
32. No medicine is nice;
Senna is a medicine.
33. Some circulars are not read with pleasure;
No begging-letters are read with pleasure.
34. All Britons are brave;
No sailors are cowards.
35. Nothing intelligible ever puzzles me;
Logic puzzles me.
36. Some pigs are wild;
All pigs are fat.
37. All wasps are unfriendly;
All unfriendly creatures are unwelcome.
38. No old rabbits are greedy;
All black rabbits are greedy.
39. Some eggs are hard-boiled;
No eggs are uncrackable.
40. No antelope is ungraceful;
Graceful creatures delight the eye.
41. All well-fed canaries sing loud;
No canary is melancholy if it sings loud.
42. Some poetry is original;
No original work is producible at will.
43. No country, that has been explored, is infested by dragons;
Unexplored countries are fascinating.
44. No coals are white;
No niggers are white.
45. No bridges are made of sugar;
Some bridges are picturesque.
46. No children are patient;
No impatient person can sit still.
47. No quadrupeds can whistle;
Some cats are quadrupeds.
48. Bores are terrible;
You are a bore.
49. Some oysters are silent;
No silent creatures are amusing.
50. There are no Jews in the house;
No Gentiles have beards a yard long.
51. Canaries, that do not sing loud, are unhappy;
No well-fed canaries fail to sing loud.
52. All my sisters have colds;
No one can sing who has a cold.
53. All that is made of gold is precious;
Some caskets are precious.
54. Some buns are rich;
All buns are nice.
55. All my cousins are unjust;
All judges are just.
56. Pain is wearisome;
No pain is eagerly wished for.
57. All medicine is nasty;
Senna is a medicine.
58. Some unkind remarks are annoying;
No critical remarks are kind.
59. No tall men have woolly hair;
Niggers have woolly hair.
60. All philosophers are logical;
An illogical man is always obstinate.
61. John is industrious;
All industrious people are happy.
62. These dishes are all well-cooked;
Some dishes are unwholesome if not well-cooked.
63. No exciting books suit feverish patients;
Unexciting books make one drowsy.
64. No pigs can fly;
All pigs are greedy.
65. When a man knows what he’s about, he can detect a sharper;
You and I know what we’re about.
66. Some dreams are terrible;
No lambs are terrible.
67. No bald creature needs a hairbrush;
No lizards have hair.
68. All battles are noisy;
What makes no noise may escape notice.
69. All my cousins are unjust;
&nbs
p; No judges are unjust.
70. All eggs can be cracked;
Some eggs are hard-boiled.
71. Prejudiced persons are untrustworthy;
Some unprejudiced persons are disliked.
72. No dictatorial person is popular;
She is dictatorial.
73. Some bald people wear wigs;
All your children have hair.
74. No lobsters are unreasonable;
No reasonable creatures expect impossibilities.
75. No nightmare is pleasant;
Unpleasant experiences are not eagerly desired.
76. No plumcakes are wholesome;
Some wholesome things are nice.
77. Nothing that is nice need be shunned;
Some kinds of jam are nice.
78. All ducks waddle;
Nothing that waddles is graceful.
79. Sandwiches are satisfying;
Nothing in this dish is unsatisfying.
80. No rich man begs in the street;
Those who are not rich should keep accounts.
81. Spiders spin webs;
Some creatures, that do not spin webs, are savage.
82. Some of these shops are not crowded;
No crowded shops are comfortable.
83. Prudent travelers carry plenty of small change;
Imprudent travelers lose their luggage.
84. Some geraniums are red;
All these flowers are red.
85. None of my cousins are just;
All judges are just.
86. No Jews are mad;
All my lodgers are Jews.
87. Busy folk are not always talking about their grievances;
Discontented folk are always talking about their grievances.
88. None of my cousins are just;
No judges are unjust.
89. All teetotalers like sugar;
No nightingale drinks wine.
90. No riddles interest me if they can be solved;
All these riddles are insoluble.
91. All clear explanations are satisfactory;
Some excuses are unsatisfactory.
92. All elderly ladies are talkative;
All good-tempered ladies are talkative.
93. No kind deed is unlawful;
What is lawful may be done without scruple.
94. No babies are studious;
No babies are good violinists.
95. All shillings are round;
All these coins are round.
96. No honest men cheat;
No dishonest men are trustworthy.
97. None of my boys are clever;
None of my girls are greedy.
98. All jokes are meant to amuse;
No Act of Parliament is a joke.
99. No eventful tour is ever forgotten;
Uneventful tours are not worth writing a book about.
100. All my boys are disobedient;
All my girls are discontented.
101. No unexpected pleasure annoys me;
Your visit is an unexpected pleasure.
EX6§ 6.
Trios of Abstract Propositions, proposed as Syllogisms: to be examined.
1.
Some x are m;
No m are y′.
Some x are y.
2.
All x are m;
No y are m′.
No y are x′.
3.
Some x are m′;
All y′ are m.
Some x are y.
4.
All x are m;
No y are m.
All x are y′.
5.
Some m′ are x′;
No m′ are y.
Some x′ are y′.
6.
No x′ are m;
All y are m′.
All y are x′.
7.
Some m′ are x′;
All y′ are m′.
Some x′ are y′.
8.
No m′ are x′;
All y′ are m′.
All y′ are x.
9.
Some m are x′;
No m are y.
Some x′ are y′.
10.
All m′ are x′;
All m′ are y.
Some y are x′.
11.
All x are m′;
Some y are m.
Some y are x′.
12.
No x are m;
No m′ are y′.
No x are y′.
13.
No x are m;
All y′ are m.
All y′ are x′.
14.
All m′ are x′;
All m′ are y.
Some y are x′.
15.
Some m are x′;
All y are m′.
Some x′ are y′.
16.
No x′ are m;
All y′ are m′.
Some y′ are x.
17.
No m′ are x;
All m′ are y′.
Some x′ are y′.
18.
No x′ are m;
Some m are y.
Some x are y.
19.
Some m are x;
All m are y.
Some y are x′.
20.
No x′ are m′;
Some m′ are y′.
Some x are y′.
21.
No m are x;
All m are y′.
Some x′ are y′.
22.
All x′ are m;
Some y are m′.
All x′ are y′.
23.
All m are x;
No m′ are y′.
No x′ are y′.
24.
All x are m′;
All m′ are y.
All x are y.
25.
No x are m′;
All m are y.
No x are y′.
26.
All m are x′;
All y are m.
All y are x′.
27.
All x are m;
No m are y′.
All x are y.
28.
All x are m;
No y′ are m′.
All x are y.
29.
No x′ are m;
No m′ are y′.
No x′ are y′.
30.
All x are m;
All m are y′.
All x are y′.
31.
All x′ are m′;
No y′ are m′.
All x′ are y.
32.
No x are m;
No y′ are m′.
No x are y′.
33.
All m are x′;
All y′ are m.
All y′ are x′.
34.
All x are m′;
Some y are m′.
Some y are x.
35.
Some x are m;
All m are y.
Some x are y.
36.
All m are x′;
All y are m.
All y are x′.
37.
No m are x′;
All m are y′.
Some x are y′.
38.
No x are m;
No m are y′.
No x are y′.
39.
No m are x;
Some m are y′.
Some x′ are y′.
40.
No m are x′;
Some y are m.
Some x are y.
EX7§ 7.
Trios of Concrete Propositions, proposed as Syllogisms: to be examined.
1. No doctors are enthusiastic;
You are enthusiastic.
You are not a doctor.
2. Dictionaries are useful;
>
Useful books are valuable.
Dictionaries are valuable.
3. No misers are unselfish;
None but misers save egg-shells.
No unselfish people save egg-shells.
4. Some epicures are ungenerous;
All my uncles are generous.
My uncles are not epicures.
5. Gold is heavy;
Nothing but gold will silence him.
Nothing light will silence him.
6. Some healthy people are fat;
No unhealthy people are strong.
Some fat people are not strong.
7. “I saw it in a newspaper.”
“All newspapers tell lies.”
It was a lie.
8. Some cravats are not artistic;
I admire anything artistic.
There are some cravats that I do not admire.
9. His songs never last an hour;
A song, that lasts an hour, is tedious.
His songs are never tedious.
10. Some candles give very little light;
Candles are meant to give light.
Some things, that are meant to give light, give very little.
11. All, who are anxious to learn, work hard;
Some of these boys work hard.
Some of these boys are anxious to learn.
12. All lions are fierce;
Some lions do not drink coffee.
Some creatures that drink coffee are not fierce.
13. No misers are generous;
Some old men are ungenerous.
Some old men are misers.
14. No fossil can be crossed in love;
Complete Works of Lewis Carroll Page 107
