68 CHAPTER 2 Sets In Exercises 15–24, let = = = U A B {1, 2, 3, 4, 5, 6, 7, 8} {1, 2, 4, 5, 7} {2, 3, 5, 6} Determine the following. 15. A B > {2, 5} 16. A B < {1, 2, 3, 4, 5, 6, 7} 17. ′ ′ A B > {8} 18. ′ A B ( ) < {8} 19. ′ A B B ( ) < > { } 20. ′ A B A B ( ) ( ) < > < { } 21. ′ ′ ′ B A B A ( ) ( ) < > < {8} 22. ′A A B ( ) < > {2, 3, 5, 6, 8} 23. − ′ A B ( ) {2, 3, 5, 6, 8} 24. ′ − ′ A B {3, 6} In Exercises 25–34, let = = = = U abcdef ghijk A a c d f g i B b c d f g C a b f i j {, , , , , , , , , , } {,, ,,,} {, , , , } {, , ,,} Determine the following. 25. − A B a i { , } 26. − B A b{ } 27. ′ ′ A B < a b e h i j k {, , , , , , } 28. ′ A C ( ) > b c d e g h j k {, , , , , , , } 29. A B ( ) C > < a b c d f g i j {,,, ,,,,} 30. ′ A C B ( ) < > acdef ghijk {, , , , , , , , , } 31. ′A C A B ( ) ( ) < < > abcdef ghijk {, , , , , , , , , , }, or 32. ′ C B A B ( ) ( ) > > > b{ } 33. − ′ − A B C ( ) c d e g h k {, , , , , } 34. − ′ − C A B ( ) a e h i k {, , , , } In Exercises 35– 44, use the Venn diagram in Fig. 2.12 to list the set of elements in roster form. U A B d i j a b e c f h g Figure 2.12 35. A a b e g h {, , , , } 36. B b c e f {, , , } 37. A B > b e {, } 38. U abcdef ghij {,,, ,,,,,,} 39. A B < a b c e f g h {, , , , , , } 40. ′ A B ( ) < d i j { , , } 41. ′ ′ A B > d i j { , , } 42. ′ A B ( ) > a c d f g h i j {,, ,,,,,} 43. − A B a g h {, , } 44. − ′ A B b e {, } U In Exercises 45–54, use the Venn diagram in Fig. 2.13 to list the set of elements in roster form. U A B 1 8 2 9 3 5 6 7 4 10 11 Figure 2.13 45. A {1, 2, 7, 8, 9} 46. B {2, 3, 5, 6, 9} 47. U {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} 48. A B > {2, 9} 49. ′A B < {2, 3, 4, 5, 6, 9, 10, 11} 50. ′ A B < {1, 2, 4, 7, 8, 9, 10, 11} 51. ′A B > {3, 5, 6} 52. ′ A B ( ) < {4, 10, 11} 53. ′ − A B {4, 10, 11} 54. − ′ A B ( ) {2, 3, 4, 5, 6, 9, 10, 11} In Exercises 55– 60, let = = A B a b {1, 2, 3} {, } 55. Determine × A B. a b a b a b {(1, ), (1, ), (2, ), (2, ), (3, ), (3, )} 56. Determine × B A. a a a b b b {( , 1), ( , 2), ( , 3), ( , 1), ( , 2), ( , 3)} 57. Does × = × A B B A? 58. Determine × n A B ( ). 6 59. Determine × n B A ( ). 6 60. Does × = × n A B n B A ( ) ( )? Yes In Exercises 61–70, let = | ∈ < = | ∈ < = | ∈ < = | ∈ < U x x N x A x x N x x B x x N x x C x x N x { and 10} { and is odd and 10} { and is even and 10} { and 6} Determine the following. 61. A B > {} 62. A B < {1, 2, 3, 4, 5, 6, 7, 8, 9}, or U 63. ′ B C ( ) < {7, 9} 64. ′ A C> {7, 9} 65. ′ − ′ A C {2, 4} 66. − ′ A C ( ) {1, 2, 3, 4, 5, 6, 8} 67. A C B ( ) < > {2, 4} 68. ′ A B C ( ) > < {1, 2, 3, 4, 5, 6, 7, 8, 9}, or U 69. ′ ′ A B C ( ) < > {1, 2, 3, 4, 5}, or C 70. ′A C A B ( ) ( ) > < > {2, 4} Problem Solving 71. Let U represent the set of retail stores in the United States. Let A represent the set of retail stores that sell children’s clothing. Describe ′A. The set of retail stores in the United States that do not sell children’s clothing 57. No. The ordered pairs are not the same. For example ≠ a a (1, ) ( ,1).
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