CHAPTER 2 Test 95 Test CHAPTER 2 In Exercises 1–8, state whether each statement is true or false. If the statement is false, explain why. 1. y {2, , ,$} Δ is equivalent to t{ , #, 6, }. True 2. = {apple, peach, orange, pear} {bean, carrot, broccoli, cauliflower} False; the sets do not contain the same elements. 3. {star, moon, sun} {star, moon, sun, planet} , True 4. ∈ | ∈ < x x N x 7 { and 7} False; the second set does not contain the element 7. 5. p q r s { , , , } has 15 subsets. False; the set has 2 , 4 or 16, subsets. 6. If = A B {}, > then A and B are disjoint sets. True 7. For any set A, ′ = A A {}. < False; for any set ′ = A A A U , , < not { }. 8. For any set A, = A U A. > True In Exercises 9 and 10, use set = | ∈ < A x x N x { and 12} 9. Write set A in roster form. = A {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} 10. Write a description of set A. Set A is the set of natural numbers less than 12. In Exercises 11–16, use the following information. = = = = U A B C {2, 4, 6, 8, 10, 12, 14} {2, 4, 6, 8} {6, 8, 10, 12} {2, 10, 14} Determine the following. 11. A B > {6, 8} 12. ′ A C< {2, 4, 6, 8, 12} 13. ′ A B C ( ) > > {6, 8} 14. ′ n A B ( ) > 2 15. − A B {2, 4} 16. × A C 16. {(2, 2), (2, 10), (2, 14), (4, 2), (4, 10), (4, 14), (6, 2), (6, 10), (6, 14), (8, 2), (8, 10), (8, 14)} 17. Using the sets provided for Exercises 11–16, draw a Venn diagram illustrating the relationship among the sets. * 18. Use a Venn diagram to determine whether ′ = ′ A B C A B A C ( ) ( ) ( ) > < > < > for all sets A, B, and C. Show your work. Equal 19. Water Activities A survey of 155 residents of Lake Placid were asked what kind of activities they participated in on a daily basis during the summer months. The following information was determined. 107 swam. 90 fished. 76 walked. 57 swam and fished. 54 swam and walked. 52 fished and walked. 35 swam, fished, and walked. Construct a Venn diagram and then determine the number of residents who participated in a) exactly two of these activities. 58 b) none of these activities. 10 c) at least one of these activities. 145 d) swimming and fishing, but not walking. 22 e) swimming or fishing, but not walking. 69 f) only fishing. 16 20. Show that the following set is infinite by setting up a one-to-one correspondence between the set and a proper subset of itself. * … + n {7, 8, 9, 10, , 6, ...} *See Instructor Answer Appendix
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