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 † 2db0 † 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.