ANSWERS A-9 33. If the sky is clear then we see the moon. 35. If Garrett does not go apple picking, then he does not go on a hayride. 37. We go to Chicago and we do not go to Navy Pier. 39. It is false that if the water is cold then I go swimming. 41. Amazon has a sale and we will not buy $100 worth of books. 43. Converse: If you are on the president’s list, then you got straight A’s. Inverse: If you did not get straight A’s, then you are not on the president’s list. Contrapositive: If you are not on the president’s list, then you did not get straight A’s. 45. Converse: If I go shopping, then Kohl’s has a sale. Inverse: If Kohl’s does not have a sale, then I do not go shopping. Contrapositive: If I do not go shopping, then Kohl’s does not have a sale. 47. Converse: If I do not stay on my diet, then the menu includes calzones. Inverse: If the menu does not include calzones, then I stay on my diet. Contrapositive: If I stay on my diet, then the menu does not include calzones. 49. If a natural number is not divisible by 7, then the natural number is not divisible by 14. True. 51. If a natural number is not divisible by 6, then the natural number is not divisible by 3. False. 53. If two lines are not parallel, then the two lines intersect in at least one point. True. 55. b) and c) are equivalent. 57. a) and c) are equivalent. 59. b) and c) are equivalent. 61. b) and c) are equivalent. 63. None are equivalent. 65. None are equivalent. 67. a) and c) are equivalent. 69. True. If p q → is false, it must be of the form T F. → Therefore, the converse must be of the form F T, → which is true. 71. False. A conditional statement and its contrapositive always have the same truth values. 73. Answers will vary. 75. a) 0.75 b) 0.80 c) 0.20 d) 0.25 e) 0.95 f) 0.95 76. 17 20 14 23 15 12 18 14 11 9 16 6 11 16 12 30 7 9 2 8 1 7 2 5 6 1 8 9 7 2 3 1 8 7 5 7 6 7 9 7 8 9 6 8 1 5 9 7 8 4 7 9 3 8 6 1 7 3 4 8 3 9 9 9 3 9 6 4 12 6 17 13 21 34 22 16 3 15 11 4 22 12 16 9 16 19 11 15 16 19 17 22 11 25. → ∧ p q r ( ) T F F F T T T T 27. ↔ ∨ p q r ( ) T T T F T F T T 29. ∼ → ∨ p q r ( ) T T T T T T T F 31. Tautology 33. Self-contradiction 35. Neither 37. Not an implication 39. Implication 41. Implication 43. True 45. False 47. True 49. True 51. True 53. False 55. True 57. False 59. True 61. False 63. False 65. True 67. False 69. No, the statement only states what will occur if your sister gets straight A’s. If your sister does not get straight A’s, your parents may still get her a computer. 71. F F T T T F F F 73. a) T F F F T F F F T F F F T T T T b) T F F T T T T T T T T T T T T T 74. Allen was born in January. Booker was born in February. Chris was born in March. Dennis was born in April. 75. Tiger Boots Sam Sue Blue Yellow Pink Green Nine Lives Whiskas Friskies Meow Mix 76. Katie was born last. Katie and Mary are saying the same thing. SECTION 3.4, PAGE 140 Answer to Recreational Math on page 133 22 4 45 11 14 15 12 22 14 17 16 15 30 9 17 17 45 9 2 1 1 1 8 5 8 8 9 2 2 1 1 7 6 9 2 4 3 5 1 3 8 2 1 9 3 4 6 7 7 9 4 7 2 5 1 7 8 6 9 6 3 9 9 8 3 8 3 7 9 9 6 8 4 1 4 3 8 1 2 6 4 19 17 9 15 3 16 17 7 33 13 6 6 11 1 5 26 6 28 3 15 14 12 16 8 5 1. Equivalent 3. ∼ ∨ p q 5. q p → 7. q p ∼ → ∼ 9. Equivalent 11. Equivalent 13. Not equivalent 15. Equivalent 17. Not equivalent 19. Equivalent 21. Not equivalent 23. Equivalent 25. Kenny Chesney does not sing country or Drake does not sing opera. 27. It is false that the cat was a Persian or the cat was a Siamese. 29. If I am late for class, then it is false that I will get bonus points and I will not fail the test. 31. I do not see a movie or I buy popcorn.
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