Exercise 1 (10 points) Give a direct proof, an indirect proof, and a proof by contradiction of the statement "if n is odd, then n + 7 is even."

Exercise 2 (10 points) Let A = {1, 2} and B = {2, 3}. Define P(A T B), P(A), and P(A S B), where P(C) indicates the power set of the set C.

Exercise 3 (40 points: 10 points for each part) Let A, B, and C be three sets in a universe U. Show the following identities:

a) (A S B) T (A T B) = (A B) S (B A)

b) (A B) S (C B) = (A S C) B

c) (A B) (A C) = A T C B

d) (A B) C = (A C) (B C)