A-4 ANSWERS 25. U A B ROC Germany Canada U.S. Norway Sweden Austria Japan Netherlands Italy China Switzerland C 27. IV 29. V 31. VIII 33. VI 35. III 37. III 39. V 41. II 43. VII 45. I 47. VIII 49. VI 51. Yes 53. No 55. No 57. No 59. Yes 61. Yes 63. Yes 65. A B ( )′ < 67. A B C ( ) ′ < > 69. a) Both equal {1, 2, 4, 5, 7, 8} b) Answers will vary. 71. U A 2.5% 0.5% 1% 5% 31% 15% 42% 3% Rh B 73. a) U A: construction projects B: plumbing projects III I V II IV VI VII VIII C: budget greater than $300,000 b) V; A B C > > c) VI; A B C ′ > > d) I; A B C ′ ′ > > 75. > > > > > > > > > > > > > > > > A B C A B C A B C A B C A B C A B C A B C A B C I: , II: , III: , IV: , V: , VI: , VII: , VIII: , ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ ′ 77. a) A B U D C IV V VI III II I VII VIII IX XIII X XI XII XIV XV XVI 87. a) {USDC, ADA} b) {BTC, ETH, BNB, USDC, XRP, ADA, DOGE, MATIC} 89. 32 customers 91. 63 members 93. A set and its complement will always be disjoint. For example, if U {1, 2, 3} = and A {1, 2}, = then A {3}, ′ = and A A {}. ′ = > 95. a) 8 4 6 2 = + − b) Answers will vary. c) Answers will vary. 97. {1, 2, 3, 4, . . .}, or A 99. {2, 4, 6, 8, . . .}, or C 101. {2, 4, 6, 8, . . .}, or C 103. {0, 1, 2, 3, 4, . . .}, or U 105. ∅ 107. A 109. U 111. B A# 113. A and B are disjoint sets. SECTION 2.4, PAGE 76 1. 8 3. a) A B ′ ′ > b) A B ′ ′ < 5. U A B b f, h e d a, c g i j C 7. U A B 7 3 1 2 4 8 6 9 5 10 C 9. U A B J, L F, O R B, S W E H C 11. U A B F, K S N T C A, D, V C H 13. {1, 3, 4, 5, 9, 10} 15. {4, 5, 6, 8, 9, 11} 17. {3, 4, 5} 19. {1, 2, 3, 7, 9, 10, 11, 12, 13, 14} 21. {2, 7, 12, 13, 14} 23. {2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14}
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