CS 381 Solutions to Homework 6

p. 45

4. B asmd C are a subdset of A and C is a subset of D.

7 (b) T (c) F (e) T (f) F

10. Let A = the empty set and B = {A}.

13. a) $\{ \emptyset , \{ a \} \}$
b) $\{ \emptyset , \{ a \}, \{ b \}, \{ a, b \} \}$
c) $\{ \emptyset , \{ \emptyset \}, \{\{ \emptyset \}\}, \{ \emptyset, \{ \emptyset \}\}\}$

14. Yes. Consider the singletons.

16 b) It is the power set of $\{ a \}$
c) It can not be a power set for it has three elements.



p. 54

19 b) A is a subset of B.
d) A and B can be any arbitrary sets because this relation holds for any sets.

20 a) No. If A and B are subsets of C, then this equality holds regardless of the relationship between A and B.
b) No. A and B may differ outside C.