Symbolic Logic I

Propositional Logic Symbolization Exercises

Put each of the following English sentences into proper symbolic notation.  Use the first letter of the italicized words as the statement letters for the simple statements in which those words occur.  Remember, statement letters stand for complete simple statements, not for words.

1. Achilles and Jason sought the fleece, but Geronimo didn't.

2. Either Guy and Fred or Nancy and Linda protested the company.

3. Juanita will not attend the party unless Damon accompanies her.

4. The customers won't be happy unless we discount our products.

5. Neither Safeway nor Larry's carries frozen watermelon chunks.

6. Neither Hutchin's nor 4th Street Market hires disabled people.

7. If either Withers or Jackson is nominated by the Green Party, then the Republicans are the sure winners.

8. Either Will or Lisa will get the Southeast "crud", but not both.

9. Will and Lisa won't both get the "crud".

10. Abe might not race, but Ted as well as Harriet and Yolanda will.

11. Yugoslavia will fall if more people write the truth about its leader.

12. If truth is relative, then both Iran and Bolivia are safe.

13. On the condition that Moscow signs a treaty with Hong Kong, the U.S. is safe.

14. East Germany will give up communism only if Bulgaria does.

15. Scotland siding with Ulster would imply that England must withdraw.

16. It's false that if the I.R.A. is a terrorist group, then England will be safe.

17. If Clinton isn't sincere, then neither is the Secretary of State.

18. Dole owns Hawaii if Del Monte owns Kansas and IBM owns New Jersey.

19. The Pacers will not beat the Knicks unless they acquire Wallace in a trade.

20. Tax cuts increase government revenue only if tax cuts spark investment.

21. Abortion is right if and only if capital punishment is right. (A, C)

22. Neither the Canswood merger nor the Alcantra acquisition will go though unless the FTC and the DOJ both sign off on the deals. (C, A, F, W)

23. Williams and Jacobs will not both be nominated for the position. (W, J)

24. Only if penguins are intelligent do they have rights. (I, R)

25. Being able to read doesn't imply self-consciousness, and vice-versa.

26. Being beautiful is a sufficient condition for being popular.

27. Professional journals are not both objective and goal-related.

28. Jesse and either Tom or Sue will talk, but only if Hugh does and Ben doesn't.

29. While the current budget crisis is taking its toll on the emotions of the people who work at the University, things will be settled by March of next year.

30. Being French was a sufficient condition for defending France against the Nazis, but it was not a necessary condition.

31. Either all professors should receive equal pay for equal work, or some should receive more pay because they are the best teachers; but no professor should receive less pay for equal work simply because of political machinations.

32. If Dolby creates a new sound device, and if Sony creates a new sound device, then if Panasonic wants to compete in the market place with Sony, then Panasonic will try to buy out Dolby.

33. Carlos Santana won't ever record any album better than "Blues for Salvador"; but if he did, he would go straight into the Musician's Hall of Fame.

34. Britain's "Mind Association" will disband only if they can't find a president as well known and well respected as the late Gilbert Ryle.

35. The beaches in Southern California are more crowded every year, and this implies that more swimmers will drown if more lifeguards are not hired.

36. If Jim goes on the Ultra-Slim Fast diet and Pat starts lifting weights, then if Brian and Lisa get back from their honeymoon in time for Brian to play in the Over-the-Line tournament, then the Oxnard Nards will be the champions.

37. Pete Rose will be voted into the Baseball Hall of Fame just in case either the Commissioner changes his mind, or the Sports Writes abandon all dignity.

38. Pete Rose will not be voted into the Baseball Hall of Fame unless one of two things happen, viz., the baseball writers lose sight of the real purpose of the Hall of Fame or they get paid off for voting for Rose.

39. The Taliban's need for additional resources is a necessary, but not sufficient, condition for it to allow the resumption of opium cultivation in Afghanistan. (T, O)

40. The Taliban will not allow the resumption of opium cultivation in Afghanistan if either Mullah's refuse permission or the citizens of Afghanistan develop a taste for heroine. (O, M, C)

41. Space being curved is a necessary and sufficient condition for the current theory of quantum mechanics being true.

42. Space being curved is a sufficient and necessary condition for the current theory of quantum mechanics being true.

43. That the current theory of quantum mechanics is true implies and is implied by the fact that space is curved.

44. It is not the case that the truth of the creationist theory of the origins of the universe is a necessary and sufficient condition for the truth of many Christian religions.

45. If either Hume or Locke was right about abstract ideas, then both Moore and Russell, and either Kripke or Quine will be vindicated in their ideas about the nature of reference.

46. The Marlboro Man has just one lung now, and he'll lose the other one if he doesn't stop smoking.

47. Neap tide will occur in three hours just in case El Nino waters don't push as far north as Mazatlan.

48. A body will remain in motion provided it is unimpeded; yet a body at rest will remain at rest unless unimpeded.

49. The Braves not winning the World Series is not a sufficient condition for moving out of Georgia. (B, G)

50. Although the Southern Ocean is beautiful, it is a godforsaken sea. (B, G)

51. Even though being a full professor implies that you're a professional, it is not the case that being a full professor is a necessary condition for being a professional.

52. The number of planets is nine, which implies that the number of planets is odd. (N, O)

53. Jon, Kate, Byron and Nezzy will each volunteer at the Resource Center, and if any two volunteer, then a large monetary donation will be made anonymously. (J, K, B, N, D)

ANSWERS