CHAPTER 2 Review Exercises 93 16. Set B is the set of states that border Kansas. = B {Colorado, Nebraska, Missouri, Oklahoma} Kansas Colorado Nebraska Missouri Oklahoma 17. = | ∈ < C x x N x { and 175} C {1, 2, 3, 4, , 174} = … 18. = | ∈ < ≤ D x x N x { and 8 80} D {9, 10, 11, 12, , 80} = … In Exercises 19–22, express each set in set-builder notation. 19. Set A is the set of natural numbers between 50 and 150. = | ∈ < < A x x N x { and 50 150} or = | ∈ ≤ ≤ A x x N x { and 51 149} 20. Set B is the set of natural numbers greater than 42. = | ∈ > B x x N x { and 42} 21. Set C is the set of natural numbers less than 7. = | ∈ < C x x N x { and 7} 22. Set D is the set of natural numbers between 27 and 51, inclusive. = | ∈ ≤ ≤ D x x N x { and 27 51} In Exercises 23–26, express each set with a written description. 23. A x x { is a capital letter of the English alphabet from E through M inclusive} = | Set A is the set of capital letters in the English alphabet from E through M, inclusive. 24. = B {penny, nickel, dime, quarter, half-dollar} Set B is the set of U.S. coins with a value of less than a dollar. 25. = C a b c {, , } Set C is the set of the first three lowercase letters in the English alphabet. 26. = | ≤ < D x x { 3 9} Set D is the set of numbers greater than or equal to 3 and less than 9. In Exercises 27–36, let U A B C {1, 2, 3, 4, , 10} {1, 3, 5, 7} {3, 7, 9, 10} {1, 7, 10} = … = = = Determine the following. 27. A B > {3, 7} 28. ′ A B < {1, 2, 3, 4, 5, 6, 7, 8} 29. ′A B > {9, 10} 30. ′ A B C ( ) < < {1, 2, 4, 6, 7, 8, 10} 31. − A B {1, 5} 32. − ′ A C {1, 7} 33. × A C {(1, 1), (1, 7), (1, 10), (3, 1), (3, 7), (3, 10), (5, 1), (5, 7), (5, 10), (7, 1), (7, 7), (7, 10)} 34. × B A {(3, 1), (3, 3), (3, 5), (3, 7), (7, 1), (7, 3), (7, 5), (7, 7), (9, 1), (9, 3), (9, 5), (9, 7), (10, 1), (10, 3), (10, 5), (10, 7)} 35. The number of subsets of set B 16 36. The number of proper subsets of set A 15 *See Instructor Answer Appendix 37. For the following sets, construct a Venn diagram and place the elements in the proper region. * U A B C {lion, tiger, leopard, cheetah, puma, lynx, panther, jaguar} {tiger, puma, lynx} {lion, tiger, jaguar, panther} {tiger, lynx, cheetah, panther} = = = = U A k d g a B c f e b h C i, j l Figure 2.29 38. A C< b c d e f h k l {,, ,,,,,} 39. ′ A B > e k {, } 40. A B C < < abcdef ghkl {,,, ,,,,,,} 41. A B C > > f { } 42. A B C ( ) < > c e f {, , } 43. − ′ A B d f l { , , } Construct a Venn diagram to determine whether the following statements are true for all sets A, B, and C. 44. ′ ′ ′ = A B A B ( ) < > True 45. ′ ′ = ′ A B A C A B C ( ) ( ) ( ) < < < < > True In Exercises 46–52, use the following table, which shows the amount of sugar, in grams (g), and caffeine, in milligrams (mg), in an oz 8- serving of selected beverages. Let the beverages listed represent the universal set. Beverage Sugar (grams, g) Caffeine (milligrams, mg) Mountain Dew 31 37 Coca-Cola 27 23 Pepsi 27 25 Sprite 26 0 Brewed coffee 0 108 Brewed tea 0 47 Orange juice 24 0 Grape juice 40 0 Gatorade 14 0 Red Bull 26 76 Arizona Lemon Iced Tea 24 15 Vitamin Water 13 17 Water 0 0 Source: IFIC.com In Exercises 38–43, use Fig. 2.29 to determine the sets.
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