ANSWERS A-7 Chapter 3 Answer to Recreational Math on page 100 1 4 8 5 3 7 9 6 2 6 5 7 3 4 1 2 3 4 8 8 6 9 1 5 7 2 4 2 3 6 9 8 6 4 1 9 7 5 1 7 6 4 3 8 9 4 9 2 2 5 2 7 8 3 9 3 7 6 9 5 8 5 2 4 1 5 1 1 4 7 3 6 8 1 9 2 5 3 6 7 8 SECTION 3.1, PAGE 104 1. Statement 3. Compound 5. a) Not b) And c) Or 7. Some flowers are not perennials. 9. All turtles have claws. 11. Some bicycles have three wheels. 13. No pedestrians are in the crosswalk. 15. Some mountain climbers are teachers. 17. Simple statement 19. Compound; biconditional, ↔ 21. Compound; conjunction, ∧ 23. Compound; conditional, → 25. Compound; negation, ∼ 27. p q ∧ 29. ∼ ∨ ∼ q p 31. ∼ → ∼ p q 33. ∧ ∼ p q 35. q p ∼ ↔ 37. p q ( ) ∼ ∨ 39. Brie does not have a MacBook. 41. Joe has an iPad and Brie has a MacBook. 43. If Joe does not have an iPad, then Brie has a MacBook. 45. Joe does not have an iPad or Brie does not have a MacBook. 47. It is false that Joe has an iPad and Brie has a MacBook. 49. p q r ( ) ∧ ∼ ∧ 51. p q r ( ) ∧ ∨ 53. r q p ( ) ∧ → 55. r q p ( ) ↔ ∧ 57. The water is 70° or the sun is shining, and we do not go swimming. 59. The water is not 70°, and the sun is shining or we go swimming. 61. If we do not go swimming, then the sun is shining and the water is 70°. 63. If the sun is shining then we go swimming, and the water is 70°. 65. The sun is shining if and only if the water is 70°, and we go swimming. 67. Not permissible, you cannot have both soup and salad. The or used on menus is the exclusive or. 69. Not permissible, you cannot have both potatoes and pasta. The or used on menus is the exclusive or. 71. a) ∧ ∼ b m b) Conjunction 73. a) ∼ → ∼ w g ( ) b) Negation 75. a) f v h ( ) ∨ → b) Conditional 77. a) ↔ ∼ ∨ c f p ( ) b) Biconditional 79. a) c w s ( ) ↔ ∨ b) Disjunction 81. a) Answers will vary. b) Answers will vary. 82. 4 7 5 2 9 1 3 6 5 1 3 6 2 1 8 7 5 9 6 9 5 4 5 6 9 5 8 9 4 2 8 1 9 3 5 6 8 6 4 8 9 6 3 1 2 6 1 4 1 8 7 3 9 4 2 6 7 3 2 3 2 7 8 7 1 4 4 2 8 3 9 7 2 5 1 3 5 8 4 7 7 59. n n 1, 2, 3, 4, 5, , , 4, 9, 14, 19, 24, , 5 1, { } { } … … ↓ ↓ ↓ ↓ ↓ ↓ … − … CHAPTER TEST, PAGE 95 1. True 2. False; the sets do not contain exactly the same elements. 3. True 4. False; the second set does not contain the element 7. 5. False; the set has 2 , 4 or 16, subsets. 6. True 7. False; for any set A A A U , , ′ = < not { }. 8. True 9. A {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} = 10. Set A is the set of natural numbers less than 12. 11. {6, 8} 12. {2, 4, 6, 8, 12} 13. {6, 8} 14. 2 15. {2, 4} 16. {(2, 2), (2, 10), (2, 14), (4, 2), (4, 10), (4, 14), (6, 2), (6, 10), (6, 14), (8, 2), (8, 10), (8, 14)} 17. 4 10 12 14 2 6 8 B A C U 18. Equal 19. U 10 31 16 35 19 17 5 22 Swam Fished Walked a) 58 b) 10 c) 145 d) 22 e) 69 f) 16 20. n n 7, 8, 9, 10, 11, , 6, 8, 9, 10, 11, 12, , 7, { } { } … + … ↓ ↓ ↓ ↓ ↓ ↓ … + …
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