A-8 ANSWERS 67. ∧ ∼ p q F T F F True in case 2 69. ∨ ∼ p q T T F T True in cases 1, 2, and 4 71. ∨ ∧ r q p ( ) T T T F F F F F True in cases 1, 2, and 3 73. ∨ ∧ ∼ q p r ( ) T T F T T T F F True in cases 1, 2, 4, 5, and 6 75. a) Jasper and Lanny qualify. b) Bridgett and Brandon do not qualify, since their combined income is less than $46,000. 77. a) Xavier qualifies; the other four do not. b) Gina is returning on April 3. Kara is returning on a Monday. Christos is not staying over on a Saturday. Chang is returning on a Monday. 79. T 81. Yes T T T F T F T SECTION 3.3, PAGE 128 1. False 3. True 5. Self-contradiction 7. T T T F 9. T F F F 11. T F F F 13. T T F T 15. F T T F 17. T T T T T F F F 19. T T T F F F F T 21. T T T T F T T T 23. T T T F T T F T SECTION 3.2, PAGE 118 1. Opposite 3. False 5. F F 7. T F T T 9. F T F F 11. T F T T 13. T T T T T F T T 15. T F T T T F T F 17. F T F T T T F T 19. F F 21. T T F T 23. T F T T 25. F T F F 27. F F T F F F F F 29. T F T F T T T F 31. T F T F T F T T 33. ∧p q T F F F 35. p q T T F T ∨ ∼ 37. ∼ ∼ ∧p q ( ) T T F T 39. ∼ ∧ ∨ p q r ( ) T F T F T T T F 41. a) True b) True 43. a) False b) False 45. a) True b) False 47. a) False b) True 49. a) True b) True 51. True 53. True 55. True 57. True 59. True 61. False 63. True 65. False
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