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Math 141 Week in Review Week 5 Problem Set Answers 1. A. True B. False – R is a subset of T, but not a proper subset. C. True D. True E. True – ∅ is a subset, and a proper subset, of every set. F. True G. False – 5 is an element of S, not a proper subset. H. False – {1} is a subset of T, not an element. 1 is an element. 2. A. {6} B. {9} C. {3, 7} D. {1, 2, 4, 5, 7, 8, 10} E. ∅ 3. See the solutions file for the shaded diagrams. 4. A. The set of students who listen to country music and not to pop. B. The set of students who do not listen to rock or do listen to pop. C. C ∪ R ∪ P D. CC ∩ RC = (C ∪ R)C E. (R ∪ P) ∩ CC 5. A. 93 B. 23 C. 41 D. 70 6. A. 21 B. 179 C. 25 D. 115 7. A. 92 B. 39 C. 30 D. 65 8. 4⋅5⋅3⋅6 = 360 different sandwiches are possible 9. 25⋅515 ways to complete the test 10. A. 105 = 100,000 B. 10⋅9⋅8⋅7⋅6 = 30,240 C. 104⋅5 = 50,000 D. 9⋅8⋅7⋅6⋅2 = 6048 E. 8⋅8⋅7⋅6⋅3 = 8064 11. A. 12! = 479,001,600 B. P(12, 10) = 239,500,800 12. 12! = 6,652,800 3!3!2! 13. C(17, 4) = 2380 14. C(15, 3)⋅C(18, 5) = 3,898,440 15. A. C(25, 5) = 53,130 B. C(19, 5) = 11, 628 C. C(19, 3)⋅C(6, 2) = 14,535