19. Assume that P(A) > 0 and P(B) > 0. Prove that if P(B) = 1, then P(A|B) = P(A) for any A. Prove that if A C B, then P(B| A) = 1. 20. Assume that P(A) > 0 and P(B) > 0. Prove that if A and B are mutually exclusive, then they cannot be independent. Prove that if A and B are independent, then they cannot be mutually exclusive