94 CHAPTER 2 Sets Construct a Venn diagram and then determine how many people * a) completed the survey. 131 b) shopped only in BJ’s Wholesale Club. 32 c) shopped in BJ’s Wholesale Club and Sam’s Club, but not Costco. 10 d) shopped in BJ’s Wholesale Club or Costco, but not Sam’s Club. 65 55. Electronic Devices In a survey of 496 college students, it was determined that 356 owned an iPad. 293 owned a laptop. 285 owned a gaming system. 193 owned an iPad and a laptop. 200 owned an iPad and a gaming system. 139 owned a laptop and a gaming system. 68 owned an iPad, a laptop, and a gaming system. Construct a Venn diagram and determine how many students surveyed owned a) only an iPad. 31 b) exactly one of these devices. 74 c) a laptop and a gaming system, but not an iPad. 71 d) an iPad or a laptop, but not a gaming system. 185 e) exactly two of these devices. 328 2.6 In Exercises 56 and 57, show that the sets are infinite by placing each set in a one-to-one correspondence with a proper subset of itself. 56. … n {2, 4, 6, 8, 10, , 2 , ...} * 57. … + n {3, 5, 7, 9, 11, , 2 1, ...} * In Exercises 58 and 59, show that each set has cardinal number ℵ0 by setting up a one-to-one correspondence between the set of counting numbers and the given set. 58. … {5, 8, 11, 14, 17, } * 59. … {4, 9, 14, 19, 24, } * Let A be the set of beverages that contain at least 20g of sugar. Let B be the set of beverages that contain at least 20 mg of caffeine. Indicate in Fig. 2.30 in which region, I–IV, each of the following beverages belongs. U A B I II III IV Figure 2.30 46. Pepsi II 47. Brewed coffee III 48. Orange juice I 49. Vitamin Water IV 50. Gatorade IV 51. Mountain Dew II 52. Red Bull II *See Instructor Answer Appendix 2.5 53. Pizza Survey A pizza chain was willing to pay $1 to each person interviewed to hear the likes and dislikes of types of pizza crust. Of the people interviewed, 200 liked thin crust, 270 liked thick crust, 70 liked both, and 50 did not like either type of crust. What was the total cost of the survey? $450 54. Shopping Preferences Visitors to a shopping mall in Atlanta, Georgia, were surveyed to determine their preference for shopping in wholesale warehouse stores. The following information was determined. 58 shopped in BJ’s Wholesale Club. 49 shopped in Sam’s Club. 45 shopped in Costco. 15 shopped in BJ’s Wholesale Club and Sam’s Club. 16 shopped in BJ’s Wholesale Club and Costco. 12 shopped in Sam’s Club and Costco. 5 shopped in all three stores. 17 did not shop in any of the three stores.
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