Symb 2 - University of Toronto



Symbolization Exercises from Logic 2000

Symbolization 2: Symbolization with AND, OR and BICONDITIONAL

Symbolize each of the following sentences using the abbreviation scheme provided:

31. Ruth is tired, but she’ll pass.

P: Ruth will pass.

S: Ruth studies.

T: Ruth is tired

32. Either Ruth studies or she doesn’t pass.

P: Ruth will pass.

S: Ruth studies.

T: Ruth is tired

33. Alfred does not study logic.

S: Alfred studies logic

34. Although she's tired, Ruth will pass anyway.

P: Ruth will pass.

S: Ruth studies.

T: Ruth is tired

35. Ruth will pass if, but only if, she studies.

P: Ruth will pass.

S: Ruth studies.

T: Ruth is tired

36. Ruth is tired; nevertheless she’ll pass.

P: Ruth will pass.

S: Ruth studies.

T: Ruth is tired

37. Ruth will pass just in case she studies.

P: Ruth will pass.

S: Ruth studies.

T: Ruth is tired

38. Ruth studies only if she’s not tired.

P: Ruth will pass.

S: Ruth studies.

T: Ruth is tired

39. Either Alfred or Alonzo orders champagne.

R: Alfred orders champagne.

Z: Alonzo orders champagne.

T: Kurt orders champagne

40. Both Alfred and Alonzo order champagne.

R: Alfred orders champagne.

Z: Alonzo orders champagne.

T: Kurt orders champagne

41. Alfred is a lover of logic who organizes his time.

R: Alfred is a lover of logic.

T: Alfred organizes his time

42. Ruth is either a logician who enjoys chocolate or a mathematician who craves peanut butter.

P: Ruth is a logician.

Q: Ruth enjoys chocolate.

R: Ruth is a mathematician.

S: Ruth craves peanut butter

43. If Alfred orders champagne, then so does Alonzo; and if Kurt orders champagne, then so does Alfred.

R: Alfred orders champagne.

Z: Alonzo orders champagne.

T: Kurt orders champagne

44. Ruth won’t pass unless she studies hard.

P: Ruth will pass.

S: Ruth studies hard.

T: Ruth is tired

45. Mary will arrive at 10:30 am. unless the plane is late.

R: Mary will arrive at 10:30a.m..

T: the plane is late

46. Neither Alfred nor Alonzo orders champagne.

R: Alfred orders champagne.

Z: Alonzo orders champagne.

T: Kurt orders champagne

47. Alfred neither does well in the course nor loses track of the argument.

W: Alfred does well in the course.

T: Alfred loses track of the argument

48. Ruth will pass if, but only if, she either studies hard or isn’t tired.

P: Ruth will pass.

S: Ruth studies hard.

T: Ruth is tired

49. If Ruth studies hard, then she’ll pass provided that she isn’t tired.

P: Ruth will pass.

S: Ruth studies hard.

T: Ruth is tired

50. Either Ruth studies hard and will pass or she doesn’t (and won’t).

P: Ruth will pass.

S: Ruth studies hard.

T: Ruth is tired

51. Either Alfred or Kurt, but not both Alonzo and Kurt, orders champagne.

R: Alfred orders champagne.

Z: Alonzo orders champagne.

T: Kurt orders champagne

52. Both Alfred and Alonzo, but not Kurt, order champagne.

R: Alfred orders champagne.

Z: Alonzo orders champagne.

T: Kurt orders champagne

53. If UCLA and USC don’t both win their first games, then USC and Cal both do win their first games.

U: UCLA wins its first game.

S: USC wins its first game.

Y: Cal wins its first game.

54. Ruth studies hard unless she’s tired, in which case she doesn’t.

P: Ruth will pass.

S: Ruth studies hard.

T: Ruth is tired

55. Unless logic is difficult, Alfred will pass if he concentrates.

P: Alfred will pass.

Q: Alfred concentrates.

R: logic is difficult.

S: Alfred will secure employment.

T: the text is readable.

X: the lectures are exciting

56. If UCLA wins its first game, then USC and Cal won’t both win their first games.

U: UCLA wins its first game.

S: USC wins its first game.

Y: Cal wins its first game

57. Assuming that either logic is difficult or the text is not readable, Alfred will pass only if he concentrates.

P: Alfred will pass.

Q: Alfred concentrates.

R: logic is difficult.

S: Alfred will secure employment.

T: the text is readable.

X: the lectures are exciting

58. If neither Richard nor Tony will pass, Yiannis won’t either.

R: Richard will pass.

T: Tony will pass.

Y: Yiannis will pass

59. If USC doesn’t win its first game, then both Cal and UCLA won’t win their first games.

U: UCLA wins its first game.

S: USC wins its first game.

Y: Cal wins its first game

60. If either Tony or Yiannis will pass, then so will Richard unless he is tired.

R: Richard will pass.

T: Tony will pass.

Y: Yiannis will pass.

U: Richard is tired.

61. Either Cal wins its first game and UCLA does not win its first game or if UCLA wins its first game then USC does not win its first game.

U: UCLA wins its first game.

S: USC wins its first game.

Y: Cal wins its first game

62. Yiannis and Tony will definitely pass; Richard however, will fail if he doesn’t study (and, for that matter, will fail even if he does).

R: Richard will pass.

T: Tony will pass.

Y: Yiannis will pass.

V: Richard will study.

X: Richard will fail

63. If Ruth will pass so long as she isn’t tired, then she’ll surely pass if she studies hard.

P: Ruth will pass.

S: Ruth studies hard.

T: Ruth is tired

64. USC wins its first game provided that UCLA does not win its first game, but USC wins its first game only if Cal wins its first game.

U: UCLA wins its first game.

S: USC wins its first game.

Y: Cal wins its first game

65. Either it is not the case that Richard pays attention and does not lose track of the argument, or it is not the case that he does not take notes or fails to do well in the course.

P: Richard pays attention.

S: Richard loses track of the argument.

T: Richard takes notes.

W: Richard does well in the course

66. Given that Cal wins its first game, USC does not win its first game provided that UCLA wins its first game.

U: UCLA wins its first game.

S: USC wins its first game.

Y: Cal wins its first game

2.067-2.070 use the following abbreviation scheme:

P: Rudolf’s prayers are answered.

V: Rudolf believes in God.

X: God exists.

W: this is the best of all possible worlds.

T: everything is permitted

67. If Rudolf’s prayers are answered if he believes in God, then God exists.

68. Rudolf does not believe in God unless this is the best of all possible worlds.

69. This is not the best of all possible worlds.

70. If God does not exist, then everything is permitted.

71. Symb 2.071: Neither UCLA nor USC will win its first game unless both are willing to work harder.

U: UCLA wins its first game.

S: USC wins its first game.

Y: Cal wins its first game.

W: UCLA is willing to work harder.

R: USC willing to work harder

72. Symb 2.072: They (Richard, Tony, and Yiannis) won’t all pass.

R: Richard will pass.

T: Tony will pass.

Y: Yiannis will pass

73. Symb 2.073: Richard won’t pass, but at least one of the other two (Tony and Yiannis) will.

R: Richard will pass.

T: Tony will pass.

Y: Yiannis will pass

74. Symb 2.076: Unless either neither Sy nor Nye neigh or Bob and Babs both bray, none of them will beat Whirlaway.

P: Sy neighs.

Q: Nye neighs.

R: Bob brays.

S: Babs brays.

T: Sy will beat Whirlaway.

U: Nye will beat Whirlaway.

V: Bob will beat Whirlaway.

W: Babs will beat Whirlaway

77. Symb 2.077: Sherlock Holmes will neither play his violin nor ask Watson for the needle; nevertheless, neither he nor Watson will fail to be baffled by Moriarty.

P: Sherlock Holmes will play his violin.

Q: Sherlock Holmes will ask Watson for the needle.

R: Sherlock Holmes will be baffled by Moriarty.

S: Watson will be baffled by Moriarty

78. Symb 2.078: Although Richard will be disappointed unless the critics approve, the concert will be worthwhile if and only if the music is played well.

P: Richard will be disappointed.

R: the critics approve.

T: the concert will be worthwhile.

W: the music is played well

79. Symb 2.079: Neither Donald nor Richard is eager, but each is willing if the other is.

R: Donald is eager.

S: Richard is eager.

W: Donald is willing.

X: Richard is willing

80. Symb 2.080: C.C. will pass unless the test is both too long and too hard, provided that the instructor is neither biased nor perverse.

P: C.C. will pass.

T: the test is too long.

R: the test is too hard.

U: the instructor is biased.

V: the instructor is perverse

81. Symb 2.081: If C.C. studies logic, then he does not do well in the course only if he does not take notes and pay attention.

X: C.C. studies logic.

P: C.C. pays attention.

S: C.C. loses track of the argument.

T: C.C. takes notes.

W: C.C. does well in the course

2.082-2.085 use the following abbreviation scheme:

V: Donald is a lover of logic.

R: Donald organizes his time.

W: Donald enjoys whiskey at night.

Z: Donald enjoys Mozart in the morning

82. Donald is a lover of logic only if he does not organize his time.

83. Donald enjoys whiskey at night provided that he both enjoys Mozart in the morning and organizes his time.

84. If Donald is a lover of logic who organizes his time, then he enjoys Mozart in the morning or whiskey at night, but not both.

85. If Donald enjoys whiskey at night, then either he enjoys Mozart in the morning and organizes his time, or he does not enjoy Mozart in the morning and does not organize his time, or else he is not a lover of logic.

86. Symb 2.086: Assuming that the professor is a Communist, he will sign the loyalty oath; but if he is an idealist, he will neither sign the loyalty oath nor speak to those who do.

P: the professor is a Communist.

S: the professor will sign the loyalty oath.

T: the professor is an idealist.

Y: the professor will speak to those who do sign the loyalty oath

87. Symb 2.087: Errors will decrease in the subject’s performance just in case neither motivation is absent nor learning has not occurred.

R: Errors will decrease in the subject’s performance.

T: motivation is absent.

U: learning has occurred

88. Symb 2.088: If Bertie and Hans are playing dice together, it is the first throw of the game, and Bertie is throwing the dice, then he wins the game on the first throw if and only if he throws 7 or 11.

P: Bertie is playing dice.

Q: Hans is playing dice.

R: Bertie and Hans are playing dice together.

S: it is the first throw of the game.

T: Bertie is throwing the dice.

U: Bertie wins the game on the first throw.

V: Bertie throws 7.

W: Bertie throws 11

89. Symb 2.089: If the world is a progressively realized community of interpretation, then either quadruplicity drinks procrastination or, provided that the Nothing negates, boredom will ensue seldom more often than frequently.

W: the world is a progressively realized community of interpretation.

Q: quadruplicity drinks procrastination.

X: the Nothing negates.

R: boredom will ensue seldom more often than frequently

90. Symb 2.090: Errors will occur in the subject’s performance if and only if motivation is absent or learning has not taken place.[Ambiguous]

R: Errors will occur in the subject’s performance.

T: motivation is absent.

U: learning has occurred

92. Symb 2.092: Neither Bertie nor Hans will listen except when the other is speaking.

P: Bertie will listen.

Q: Hans will listen.

R: Bertie is speaking.

S: Hans is speaking

93. Symb 2.093: No more than one of then (Richard, Tony, and Yiannis, of course) will pass.

R: Richard will pass.

T: Tony will pass.

Y: Yiannis will pass

94. Symb 2.094: Exactly two of then (among Richard, Tony, and Yiannis) will pass.

R: Richard will pass.

T: Tony will pass.

Y: Yiannis will pass

The rest use the following abbreviation scheme:

P: Paula will pass.

Q: Quincy will pass.

R: Rachel will pass.

S: Sidney will pass.

T: Paula is tired.

U: Quincy studies hard.

V: Rachel studies hard.

W: Paula studies hard.

X: Sidney studies hard.

Y: Quincy is tired

100. Paula, who studies hard, will pass.

101. Paula won’t pass unless she studies hard.

102. Paula neither studies hard nor passes.

103. Paula will pass if, but only if, she either studies hard or isn’t tired.

104. Either Paula studies hard and will pass or she doesn’t (and won’t).

105. If Paula will pass unless she’s tired, then she’ll pass so long as she studies hard.

106. Although she’s tired, Paula will pass anyway.

107. Provided that Paula studies hard, she’ll pass just in case she isn’t tired.

108. Paula studies hard unless she’s tired, in which case (that is, if she’s tired) she doesn’t.

109. If either Quincy or Rachel will pass, then so will Paula unless she is tired.

110. Paula and Quincy study hard and will pass.

111. Unless neither Paula nor Quincy studies hard, both will pass.

112. Both Paula and Quincy won’t pass, but Rachel and Sidney won’t fail to pass.

113. Paula will pass just in case neither Quincy nor Rachel doesn’t study hard.

114. If and only if Paula is not tired, will she and Rachel pass.

115. Unless she studies hard, Paula will study hard and pass just in case Quincy does the same.

116. Quincy studies hard, but Rachel studies hard and passes.

117. Either Sidney will pass without studying hard, or on the condition that Quincy both studies hard and passes, Sidney will fail to pass.

118. Quincy, who studies hard, also will pass, unless Sidney will fail to pass only on the condition that he fails to study hard.

119. Paula will neither study hard nor pass, but either Rachel or Quincy, but not Sidney, will pass.

120. Although Paula isn’t tired, she neither studies hard nor passes; but Sidney won’t study hard and won’t pass.

121. Unless Rachel, who either failed to study hard or succeeded in passing, does pass, Sidney will neither study hard nor fail to study hard.

122. Quincy will either study hard or fail to pass, but not both; hover, Rachel studies hard just in case it is not the case that she will pass ii and only if it is the case that she will pass.

123. Paula neither studies hard, nor is tired, nor passes, but Quincy does all three.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download