Practice Exercises
In Exercises 1–4, describe a universal set U that includes all elements in the given sets. Answers may vary.
1. A = {Bach, Mozart, Beethoven}
B = {Brahms, Schubert}
2. A = {William Shakespeare, Charles Dickens}
B = {Mark Twain, Robert Louis Stevenson}
3. A = {Pepsi, Sprite}
B = {Coca-Cola, Seven-Up}
4. A = {Acura RSX, Toyota Camry, Mitsubishi Lancer}
B = {Dodge Ram, Chevrolet Impala}
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'
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.
9. A'
10. B'
11. C'
12. D'
In Exercises 13–16, let U = {1, 2, 3, 4, … },
A = {1, 2, 3, 4, …, 20}, B = {1, 2, 3, 4, …, 50},
C = {2, 4, 6, 8, … }, and D = {1, 3, 5, 7, … }.
Use the roster method to write each of the following sets.
13. A'
14. B'
15. C'
16. D'
In Exercises 17–40, let
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 3, 5, 7}
B = {1, 2, 3}
C = {2, 3, 4, 5, 6}.
Find each of the following sets.
17. A ∩ B
18. B ∩ C
19. A ∪ B
20. B ∪ C
21. A'
22. B'
23. A' ∩ B'
24. B' ∩ C
25. A ∪ C'
26. B ∪ C'
27. (A ∩ C)'
28. (A ∩ B)'
Find each of the following:
41. A ∩ B
44. B ∪ C
47. A' ∩ B'
50. B ∪ C'
53. A' ∪ C'
56. (A ∪ C)'
59. A ∩ ∅
62. B ∪ U
65. (A ∩ B) ∪ B'
In Exercises 67-78, write each set in roster form.
67. A
69. U
71. A ∩ B
73. B'
75. (A ∪ B)'
77. A ∩ B'
In Exercises 79-92, find each cardinality.
79. B
82. A ∩ B
85. n(A')