Problem 16.9

Let A and B be two sets. Prove that (A B) (A B) = .

Problem 16.10

Let A and B be two sets. Show that if A B then A Bc = .

Problem 16.11

Let A, B and C be three sets. Prove that if A B and B C = then A C =

Problem 16.12

Find two sets A and B such that A B = but A B 6= .

Problem 16.13

Suppose that A = {1, 2} and B = {2, 3}. Find each of the following:

a. P(A B).

b. P(A).

c. P(A B).

d. P(A B).

Problem 16.14

a. Find P().

b. Find P(P()).

c. Find P(P(P())).

Problem 16.15

Determine which of the following statements are true and which are false.

Prove each statement that is true and give a counterexample for each statement that is false.

a. P(A B) = P(A) P(B).

b. P(A B) = P(A) P(B).

c. P(A) P(B) P(A B).

d. P(A B) = P(A) P(B).