1. Find the power set of A, where A = { 2x is an element of Z | 7 < x < 10, x is an element of Z } .

2. Let, A = {3n is an element of Z | -1 <= n <= 3, n is an element of Z } , B = {1, 2} and C = {{1,2}}. Find A X ( B X C) .

3. Use an element argument to prove the statement:

For all sets A and B, A^c n B^c is a subset of (A u B)^c

4. For all sets A and B, simplify the given expression,

(A - (A n B)) n (B - (A n B))

Cite a property from Theorem 6.2.2 for every step of the proof.