Univ. “food”; m = wholesome; x = muffins; y = buns.
xm0 † y1m0
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 † m1y′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.
xm1 † ym0 ¶ 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′1x0 † ym0 ¶ xy0 [Fig. I.
Conclusion right.
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.
xm0 † m′y1
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.
xm0 † y1m0
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′m0 † 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.
x1m′0 † m′y0
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.
mx0 † 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.
m1x′0 † my0 ¶ 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.
m1x′0 † m′1y′0 ¶ x′y′0 [Fig. I.
Conclusion wrong: right one is “No man walks on neither.”
36. No wheelbarrows are comfortable;
No uncomfortable vehicles are popular.
No wheelbarrows are popular.
Univ. “vehicles”; m = comfortable; x = wheelbarrows; y = popular.
xm0 † m′x0 ¶ xy0 [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.
xm0 † 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.
xm0 † m1y′0 ¶ x′y1 [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.
x1m′0 † y1m0 ¶ (x1y0 † y1x0) [Fig. I (β).
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.
x1m′0 † ym′1 ¶ x′y1 [Fig. II.
Conclusion right.
SL8Solutions for § 8.
1. 1cd0 † 2a1d′0 † 3b1c′0; 1cd † 2ad′ † 3bc′ ¶ ab0 † a1 † b1
i.e. ¶ a1b0 † b1a0
2. 1d1b′0 † 2ac′0 † 3bc0; 1db′ † 3bc † 2ac′ ¶ da0 † d1 i.e. ¶ d1a0
3. 1ba0 † 2cd′0 † 3d1b′0; 1ba † 3db′ † 2cd′ ¶ ac0
4. 1bc0 † 2a1b′0 † 3c′d0; 1bc † 2ab′ † 3c′d ¶ ad0 † a1 i.e. ¶ a1d0
5. 1b′1a0 † 2bc0 † 3a′d0; 1b′a † 2bc † 3a′d ¶ cd0
6. 1a1b0 † 2b′c0 † 3d1a′0; 1ab † 2b′c † 3da′ ¶ cd0 † d1 i.e. ¶ d1c0
7. 1db′0 † 2b1a′0 † 3cd′0; 1db′ † 2ba′ † 3cd′ ¶ a′c0
8. 1b′d0 † 2a′b0 † 3c1d′0; 1b′d † 2a′b † 3cd′ ¶ a′c0 † c1 i.e. ¶ c1a′0
9. 1b′1a′0 † 2ad0 † 3b1c′0; 1b′a′ † 2ad † 3bc′ ¶ dc′0
10. 1cd0 † 2b1c′0 † 3ad′0; 1cd † 2bc′ † 3ad′ ¶ ba0 † b1 i.e. ¶ b1a0
11. 1bc0 † 2d1a′0 † 3c′1a0; 1bc † 3c′a † 2da′ ¶ bd0 † d1 i.e. ¶ d1b0
12. 1cb′0 † 2c′1d0 † 3b1a′0; 1cb′ † 2c′d † 3ba′ ¶ da′0
13. 1d1e′0 † 2c1a′0 † 3bd′0 † 4e1a0; 1de′ † 3bd′ † 4ea † 2ca′ ¶ bc0 † c1
i.e. ¶ c1b0
14. 1c1b′0 † 2a1e′0 † 3d1b0 † 4a′1c′0; 1cb′ † 3db † 4a′c′ † 2ae′ ¶ de′0 † d1
i.e. ¶ d1e′0
15. 1b′d0 † 2e1c′0 † 3b1a′0 † 4d′1c0; 1b′d † 3ba′ † 4d′c † 2ec′ ¶ a′e0 † e1
i.e. ¶ e1a′0
16. 1a′e0 † 2d1c0 † 3a1b′0 † 4e′1d′0; 1a′e † 3ab′ † 4e′d′ † 2dc ¶ b′c0
17. 1d1c′0 † 2a1e′0 † 3bd′0 † 4c1e0; 1dc′ † 3bd′ † 4ce † 2ae′ ¶ ba0 † a1
i.e. ¶ a1b0
18. 1a1b′0 † 2d1e′0 † 3a′1c0 † 4be0; 1ab′ † 3a′c † 4be † 2de′ ¶ cd0 † d1
i.e. ¶ d1c0
19. 1bc0 † 2e1h′0 † 3a1b′0 † 4dh0 † 5e′1c′0; 1bc † 3ab′ † 5e′c′ † 2eh′ † 4dh
¶ ad0 † a1 i.e. ¶ a1d0
20. 1dh′0 † 2ce0 † 3h1b′0 † 4ad′0 † 5be′0;
1dh′ † 3hb′ † 4ad′ † 5be′ † 2ce ¶ ac0
21. 1b1a′0 † 2dh0 † 3ce0 † 4ah′0 † 5c′1b′0;
1ba′ † 4ah′ † 2dh † 5c′b′ † 3ce ¶ de0
22. 1e1d0 † 2b′h′0 † 3c′1d′0 † 4a1e′0 † 5ch0;
1ed † 3c′d′ † 4ae′ † 5ch † 2b′h′ ¶ ab′0 † a1 i.e. ¶ a1b0
23. 1b′1a0 † 2de′0 † 3h1b0 † 4ce0 † 5d′1a′0;
1b′a † 3hb † 5d′a′ † 2de′ † 4ce ¶ hc0 † h1 i.e. ¶ h1c0
24. 1h′1k0 † 2b′a0 † 3c1d′0 † 4e1h0 † 5dk′0 † 6bc′0;
1h′k † 4eh † 5dk′ † 3cd′ † 6bc′ † 2b′a ¶ ea0 † e1 i.e. ¶ e1a0
25. 1a1d′0 † 1k1b�
�0 † 1e1h′0 † 1a′b0 † 5d1c′0 † 6h1k′0;
1ad′ † 4a′b † 2kb′ † 5dc′ † 6hk′ † 3eh′ ¶ c′e0 † e1 i.e. ¶ e1c′0
26. 1a′1h′0 † 2d′k′0 † 3e1b0 † 4hk0 † 5a1c′0 † 6b′d0;
1a′h′ † 4hk † 2d′k′ † 5ac′ † 6b′d † 3eb ¶ c′e0 † e1 i.e. ¶ e1c′0
27. 1e1d0 † 2hb0 † 3a′1k′0 † 4ce′0 † 5b′1d′0 † 6ac′0;
1ed † 4ce′ † 5b′d′ † 2hb † 6ac′ † 3a′k′ ¶ hk′0
28. 1a′k0 † 2e1b′0 † 3hk′0 † 4d′c0 † 5ab0 † 6c′1h′0;
1a′k † 3hk′ † 5ab † 2eb′ † 6c′h′ † 4d′c ¶ ed′0 † e1 i.e. ¶ e1d′0
29. 1ek0 † 2b′m0 † 3ac′0 † 4h′1e′0 † 5d1k′0 † 6cb0 † 7d′1l′0 † 8hm′0;
1ek † 4h′e′ † 5dk′ † 7d′l′ † 8hm′ † 2b′m † 6cb † 3ac′ ¶ l′a0
30. 1n1m′0 † 2a′1e′0 † 3c′l0 † 5k1r0 † 5ah′0 † 6dl′0 † 7cn′0 † 8e1b′0 † 9m1r′0 † 10h1d′0;
1nm′ † 7cn′ † 3c′l † 6dl′ † 9mr′ † 4kr † 10hd′ † 5ah′ † 2a′e′ † 8eb′
¶ kb′0 † k1 i.e. ¶ k1b′0
SL9Solutions for § 9.
1.
1b1d0 † 2ac0 † 3d′1c′0; 1bd † 3d′c′ † 2ac ¶ ba0 † b1, i.e. ¶ b1a0
i.e. Babies cannot manage crocodiles.
2.
1a1b′0 † 2d1c′0 † 3bc0; 1ab′ † 3bc † 2dc′ ¶ ad0 † d1, i.e. ¶ d1a0
i.e. Your presents to me are not made of tin.
3.
1da0 † 2c1b′0 † 3a′b0; 1da † 3a′b † 2cb′ ¶ dc0 † c1, i.e. ¶ c1d0
i.e. All my potatoes in this dish are old ones.
4.
1ba0 † 2b′d0 † 3c1a′0; 1ba † 2b′d † 3ca′ ¶ dc0 † c1, i.e. ¶ c1d0
i.e. My servants never say “shpoonj.”
5.
1ad0 † 2cd′0 † 3b1a′0; 1ad † 2cd′ † 3ba′ ¶ cb0 † b1, i.e. ¶ b1c0
i.e. My poultry are not officers.
6.
1c1a′0 † 2c′b0 † 3da0; 1ca′ † 2c′b † 3da ¶ bd0
i.e. None of your sons are fit to serve on a jury.
7.
1cb0 † 2da0 † 3b′1a′0; 1cb † 3b′a′ † 2da ¶ cd0
i.e. No pencils of mine are sugarplums.
8.
1cb′0 † 2d1a′0 † 3ba0; 1cb′ † 3ba † 2da′ ¶ cd0 † d1, i.e. ¶ d1c0
i.e. Jenkins is inexperienced.
9.
1cd0 † 2d′a0 † 3c′b0; 1cd † 2d′a † 3c′b ¶ ab0
i.e. No comet has a curly tail.
10.
1d′c0 † 2ba0 † 3a′1d0; 1d′c † 3a′d † 2ba ¶ cb0
i.e. No hedgehog takes in the Times.
11.
1b1a′0 † 2c1b′0 † 3ad0; 1ba′ † 2cb′ † 3ad ¶ cd0 † c1, i.e. ¶ c1d0
i.e. This dish is unwholesome.
12.
1b1c′0 † 2d′a0 † 3a′c0; 1bc′ † 3a′c † 2d′a ¶ bd′0 † b1, i.e. ¶ b1d′0
i.e. My gardener is very old.
13.
1a1d′0 † 2bc0 † 3c′1d0; 1ad′ † 3c′d † 2bc ¶ ab0 † a1, i.e. ¶ a1b0
i.e. All humming-birds are small.
14.
1c′b0 † 2a1d′0 † 3ca′0; 1c′b † 3ca′ † 2ad′ ¶ bd′0
i.e. No one with a hooked nose ever fails to make money.
15.
1b1a′0 † 2b′1d0 † 3ca0; 1ba′ † 2b′d † 3ca ¶ dc0
i.e. No gray ducks in this village wear lace collars.
16.
1d1b′0 † 2cd′0 † 3ba0; 1db′ † 2cd′ † 3ba ¶ ca0
i.e. No jug in this cupboard will hold water.
17.
1b′1d0 † 2c1d′0 † 3ab0; 1b′d † 2cd′ † 3ab ¶ ca0 † c1, i.e. ¶ c1a0
i.e. These apples were grown in the sun.
18.
1d′1b′0 † 2c1b0 † 3c′a0; 1d′b′ † 2cb † 3c′a ¶ d′a0 † d′1, i.e. ¶ d′1a0
i.e. Puppies, that will not lie still, never care to do worsted-work.
19.
1bd′0 † 2a1c′0 † 3a′d0; 1bd′ † 3a′d † 2ac′ ¶ bc′0
i.e. No name in this list is unmelodious.
20.
1a1b′0 † 2dc0 † 3a′1d′0; 1ab′ † 3a′d′ † 2dc ¶ b′c0
i.e. No M.P. should ride in a donkey-race, unless he has perfect self-command.
21.
1bd0 † 2c′a0 † 3b′c0; 1bd † 3b′c † 2c′a ¶ da0
i.e. No goods in this shop, that are still on sale, may be carried away.
22.
1a′b0 † 2cd0 † 3d′a0; 1a′b † 3d′a † 2cd ¶ bc0
i.e. No acrobatic feat, which involves turning a quadruple somersault, is ever attempted in a circus.
23.
1dc′0 † 2a1b′0 † 3bc0; 1dc′ † 3bc † 2ab′ ¶ da0 † a1, i.e. ¶ a1d0
i.e. Guinea-pigs never really appreciate Beethoven.
24.
1a1d′0 † 2b′1c0 † 3ba′0; 1ad′ † 3ba′ † 2b′c ¶ d′c0
i.e. No scentless flowers please me.
25.
1c1d′0 † 2ba′0 † 3d1a0; 1cd′ † 3da † 2ba′ ¶ cb0 † c1, i.e. ¶ c1b0
i.e. Showy talkers are not really well-informed.
26.
1ea0 † 2b1d′0 † 3a′1c0 † 4e′b′0; 1ea † 3a′c † 4e′b′ † 2bd′ ¶ cd′0
i.e. None but red-haired boys learn Greek in this school.
27.
1b1d0 † 2ac′0 † 3e1d′0 † 4c1b′0;
1bd † 3ed′ † 4cb′ † 2ac′ ¶ ea0 † e1, i.e. ¶ e1a0
i.e. Wedding-cake always disagrees with me.
28.
1ad0 † 2e′1b′0 † 3c1d′0 † 4e1a′0;
1ad † 3cd′ † 4ea′ † 2e′b′ ¶ cb′0 † c1, i.e. ¶ c1b′0
i.e. Discussions, that go on while Tomkins is in the chair, endanger the peacefulness of our Debating-Club.
29.
1d1a0 † 2e′c0 † 3b1a′0 † 4d′e0;
1da † 3ba′ † 4d′e † 2e′c ¶ bc0 † b1, i.e. ¶ b1c0
i.e. All gluttons in my family are unhealthy.
30.
1d1e0 † 2c′a0 † 3b1e′0 † 4c1d′0;
1de † 3be′ † 4cd′ † 2c′a ¶ ba0 † b1, i.e. ¶ b1a0
i.e. An egg of the Great Auk is not to be had for a song.
31.
1d′b0 † 2a1c′0 † 3c1e′0 † 4a′d0; 1d′b † 4a′d † 2ac′ † 3ce′ ¶ be′0
i.e. No books sold here have gilt edges unless they are priced at 5s. and upwards.
32.
1a′1c′0 † 2d1b0 † 3a1e′0 † 4c1b′0;
1a′c′ † 3ae′ † 4cb′ † 2db ¶ e′d0 † d1, i.e. ¶ d1e′0
i.e. When you cut your finger, you will find Tincture of Calendula useful.
33.
1d′b0 † 2a1e′0 † 3ec0 † 4d1a′0; 1d′b † 4da′ † 2ae′ † 3ec ¶ bc0
i.e. I have never come across a mermaid at sea.
34.
1c′1b0 † 2a1e′0 † 3d1b′0 † 4a′1c0;
1c′b † 3db′ † 4a′c † 2ae′ ¶ de′0 † d1, i.e. ¶ d1e′0
i.e. All the romances in this library are well-written.
35.
1e′d0 † 2c′a0 † 3eb0 † 4d′c0; 1e′d † 3eb † 4d′c † 2c′a ¶ ba0
i.e. No bird in this aviary lives on mince-pies.
36.
1d′1c′0 † 2e1a′0 † 3c1b0 † 4e′d0; 1d′c′ † 3cb † 4e′d † 2ea′ ¶ ba′0
i.e. No plum-pudding, that has not been boiled in a cloth, can be distinguished from soup.
37.
1ce′0 † 2b′a′0 † 3h1d′0 † 4ae0 † 5bd0;
1ce′ † 4ae † 2b′a′ † 5bd † 3hd′ ¶ ch0 † h1, i.e. ¶ h1c0
i.e. All your poems are uninteresting.
38.
1b′1a′0 † 2d
b0 † 3he′0 † 4ec0 † 5a1h′0;
1b′a′ † 2db † 5ah′ † 3he′ † 4ec ¶ dc0
i.e. None of my peaches have been grown in a hothouse.
39.
1c1d0 † 2h1e′0 † 3c′1a′0 † 4h′b0 † 5e1d′0;
1cd † 3c′a′ † 5ed′ † 2he′ † 4h′b ¶ a′b0
i.e. No pawnbroker is dishonest.
40.
1bd′0 † 2c′h0 † 3e1b′0 † 4da0 † 5e′c0;
1bd′ † 3eb′ † 4da † 5e′c † 2c′h ¶ ah0
i.e. No kitten with green eyes will play with a gorilla.
41.
1c1a′0 † 2h′b0 † 3ae0 † 4d1c′0 † 5h1e′0;
1ca′ † 3ae † 4dc′ † 5he′ † 2h′b ¶ db0 † d1, i.e. ¶ d1b0
i.e. All my friends in this College dine at the lower table.
42.
1ca0 † 2h1d′0 † 3c′1e′0 † 4b′a′0 † 5d1e0;
1ca † 3c′e′ † 4b′a′ † 5de † 2hd′ ¶ b′h0 † h1, i.e. ¶ h1b′0
i.e. My writing-desk is full of live scorpions.
43.
1b′1e0 † 2ah0 † 3dc0 † 4e′1a′0 † 5bc′0
1b′e † 4e′a′ † 2ah † 5bc′ † 3dc ¶ hd0
i.e. No Mandarin ever reads Hogg’s poems.
Complete Works of Lewis Carroll Page 113