Section 2.3 (Page 84, Textbook): 5,7,9,13,17,23,25,27,29,31,33,37,39,67,79

CHAPTER 2: Set Theory Practice Exercises Find each of the following sets. In Exercises 1-4, describe a universal set U that includes all 41. An B 42. Bnc 43. AUB elements in the given sets. Answers may vary. 44. BUC 45. A' 46. B' 1. A = {Beyonce, Bruno Mars, Taylor Swift } 47. A'n B' 48. B'n C 49. A UC' B = {Mariah Carey, Usher } 50. BUC' 51. (Anc) 52. (An B)' 2. A = {Larry Bird, Magic Johnson } 53. A' UC 54. A' U B' 55. (AUB)' B = { Michael Jordan, Stephen Curry } 56. (AUC)' 57. AUS 58. CUP 3. A = {Pepsi, Sprite } 59. Ane 60. Che 61. AUU B = { Coca-cola, 7 Up } 62. BUU . Anu 64. BOU 4. A = { Acura RDX, Toyota Camry, Mitsubishi Lancer } 65. (An B) UB' 66. (AUB) n B' B = {Dodge Ram, Chevrolet Impala } In Exercises 67-78, use the Venn diagram to represent each set in roster form In Exercises 5-8, let U = {a, b, c, d, e, f, g), A = {a, b, f, g } B = {c, d, e}, C = {a, g}, and D = {a, b, c, d, e, f}. Use the roster method to write each of the following sets. 5. A' 6. B' 7. C 8. D' 13 QUIN In Exercises 9-12, let U = {1, 2, 3, 4, . . . , 20}, A = {1, 2, 3, 4, 5}, B = (6, 7, 8, 9}, C = {1, 3, 5, 7, . . ., 19 }, and D = (2, 4, 6, 8, . . ., 20}. Use the roster method to write each of the following sets. 67. A 68. B 9. A' 10. B' 11. C' 12. D' 69. U 70. AUB In Exercises 13-16, let U = {1, 2, 3, 4, . . .}, 72. A' 4 = {1, 2, 3, 4, . . ., 20 }, B = {1, 2, 3, 4, . . ., 50} 71. AnB C = (2, 4, 6, 8, . . .}, and D = {1, 3, 5, 7, .. .}. Use the roster 73. B' 74. (An By' method to write each of the following sets. 75. (AUB)' 76. A'n B 13. A' 14. B 15. C' 16. D' 77. An B' 78. A UB' In Exercises 17-40, let In Exercises 79-92, use the Venn diagram to determine each set or U = {1, 2, 3, 4, 5, 6, 7} cardinality. A = {1, 3, 5, 7} B = {1, 2, 3} C = {2, 3, 4, 5, 6 }. two Find each of the following sets. six four 17. AnB 18. Bnc 19. AUB 10 20. BUC 21. A' 01 22. B' 23. A'n B' 24. B'n C 25. A UC' 79. B 80. A 81. AUB 26. BUC' 27. (Anc) 28. (An B)' 29. A' UC' 30. A' U B' 31. (AUB)' 82. An B 83. n( A U B) 84. n( An B) 32. (A UC)' 33. AUD 34. CUB 85. n( A') 86. n( B') 87. (An B)' 35 . And 36. Cne 37. AUU 88. (A UB)' 89. A'n B 90. An B' 38. BUU 39. Anu 40. BOU 91. n(U) - n(B) 92. n(U) - n( A) In Exercises 41-66, let Use the formula for the cardinal number of the union of two sets U = {a, b, c, d, e, f, g, h } to solve Exercises 93-96. A = {a, g, h } 93. Set A contains 17 elements, set B contains 20 elements, and B = {b, g, h } 6 elements are common to sets A and B. How many elements are in A U B? C = {b, c, d, e, f }. 94. Set A contains 30 elements, set B contains 18 elements, and 5 elements are common to sets A and B. How many elements are in A U B? 8432. CHAPTER 2: Set Theory . mt. t : 4U.n.rlt: 1mm: 11.tllLt = to. ntAB):.ntAC)=9,ntBC)=7. n(ABC)=2 mm = 25.n(A) = s, 14(8) = 9,n(C)=10, MAHB):6.n(AC)=9,n(BC)=8, n(ABC)=5 Application Exercises LGBTQ Tolerance We return to our discussion or: page 103 involving two Harris Polls taken in 2017 and 2018. For each year, respondents were classied by age bracket (1'8 to 34 vs. 35 to 51'} and whether they were comfortable with learning it tmily member was LGB TQ. The results ofthe surveys, indicating the number of respondents in each region, are shoer in the Venn diagram. Use these cardinalities to so fve Exercises 3338. 33. 35. 37. 39. U ram?) A (18 to 34) C (Comfortable) 300 Source: Cordinolities are based on the percentages given by the Harris Poll on behalf ofGLAAD. For the 2017 poll, how many respondents ages 18 to 34 were uncomfortable with an LGBTQ family member? For the 2017 poll. how many respondents ages 35 to 51 were comfortable with an LGBTQ family member? For the 2018 poll, how many respondents ages 18 to 34 were comfortable with an LGBTQ family member? For the 2018 poll, how many respondents ages 18 to 34 were uncomfortable with an LGBTQ family member? For the 2017 and 2018 polls combined. how many respondents ages 35 to 51 were comfortable with an LGBTQ family member? For the 2017 and 2018 polls combined. how many respondents ages 35 to 51 were uncomfortable with an LGBTQ family member? Use the following Venn diagram. 107 40. 41. 42. m: |JIL \\LtlLLllttllt. .[.. t .. \"Show. 270 people in the United States agreed with the statement. Source: Based on data from The Sociology Project 2.0. Pearson If 780 adults surveyed were in the United States, a. How many adults in Great Britain agreed with the statement? b. How many adults in Great Britain disagreed with the statement? In a survey, 1510 domestic and international travelers were asked if they agree or disagree with the following statement: It is a good idea to buy ight insurance before embarking on a trip. The results of the survey showed that 440 people agreed with the statement. 260 international travelers agreed with the statement. Use the following Venn diagram. U A I (international travelers) If 770 of the people surveyed were international travelers, a. How many domestic travelers statement? agreed with the I}. How many domestic travelers disagreed with the statement? A pollster conducting a telephone poll of a city's residents asked two questions: 1. Do you currently smoke cigarettes? 2. Regardless of your answer to question 1, would you support a ban on smoking in all city parks? a. Construct a Venn diagram that allows the respondents to the poll to be identified by whether or not they smoke cigarettes and whether or not they support the ban. I}. Write the letter b in every region of the diagram that represents smokers polled who support the ban. 1:. Write the letter c in every region of the diagram that represents nonsmokers polled who support the ban. d. Write the letter d in every region of the diagram that represents nonsmokers polled who do not support the ban. A pollster conducting a telephone poll at a college campus asked students two questions: 1. Do you binge drink three or more times per month? 2. Regardless of your answer to question 1, are you frequently behind in your school work? [:1 D