Let A = {1, 4, 0}, B = {{4}, 2, 0}, C = {2, {0, 0}}. Compute: A Union B, B Intersection C, B \(A Union C), and P(B) Intersection (P(A) Union P(C)) (here P means the power set). (b) Let A, B, C be sets. Prove that if A Union B = A Union C and A Intersection B = A Intersection C, then B = C. (c) Fix a set A of n greaterthanorequalto 1 elements. Define S(k) to be the number of subsets of A that have cardinality divisible by k. Prove that S(2) = 2^n - 1