C: ANSWERS TO SELECTED PROBLEMS
Chapter 2.1, Sets and Subsets
1. Washington, West
Virginia, Wisconsin, Wyoming.
3. This is not a
well-defined set.
5. All students with
blue eyes. All students who are
male. All students who own a dog.
7. 
.
9. [a] False, [c] True.
11. {x | you add the two adjacent elements to get the next
element between 0 and 100}
13. 6.
15. [a] 
, [c] =, [e] =.
17. Yes, the empty
set is always a subset of any set.
19. [b] and [c] are
well-defined sets.
21. B = {6, 8, 10, 12}.
23. [a] True, [c] False.
25. W = {1, 2, 3, 4}.
27. There are 29
different coin combinations.
29. 4 possible
subsets: {}, {a}, {b}, {a, b}.
31. There are 16
possible subsets.
33. 
.
35. 
.
37. 60 wolves are on
the island.
39. {(Y, Y, Y, N),
(Y, Y, N, Y), (Y, N, Y, Y), (N, Y, Y, Y), (Y, Y, Y, Y)}.
Chapter 2.2, Set Operations
1. 
.
3. C = {Jose, Beverly, Tom, Phil, Sue}.
5. {}, The empty
set.
7. 
9. 
11. 
13. [a] True, [b] True, [c] False.
15. {Nick, Linda,
Mike, Jody}.
17. 
19. W = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}.
21. 
23. S = {(H, H),
(H, T), (T, H), (T, T)}.
25. A = {1, 3, 5, 7, 9}, B = {2, 3, 5, 7}, C = {6, 7, 8, 9}.
27. 17.
29. 
Chapter 2.3, Venn Diagrams
1. 
. 3. 
.
5. 
. 7. 2.
9. No. 11. The region shaded
is outside both subsets.
13. You cannot find
the complement to any set without knowing the elements in the universal set.
15. 19. 17. 50.
19. 
21. 
23. 20. 25. 
27. 15. 29. 
31. 12. 33. 
.
35. 50.
Chapter 2.4, Chapter Review
Mastery Quiz
1. [a, c, d], 2. [b, c, d], 3. [b], 4.
[d], 5. [d], 6. [d], 7. [c], 8.
[d], 9. [a], 10. [a]
Review
1. {(c, a), (c, e),
(c, u), (u, a), (u, e), (u, u)}.
3. [a] {4, 6}, [c] {(2, 4),
(2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (5, 4), (5, 5), (5, 6), (7, 4), (7, 5),
(7,
6)}, [e] {3, 5, 7}.
5. 
, where k is the
cardinality. 7. 48.
9. 
11. 
13. 19. 15. The element 
is the only one.
17. 22. 19. [a] 40, [b] 10.
21. A = {3, 4, 5, 8,
9, 11}, B = {2, 5, 6, 8, 10}, C = {3, 6, 7, 8, 11}.