Setting the Scene. Please use set proof to answer all three parts of question. thank you

2. Setting the Scene (20 points) Prove each of the following claims for arbitrary sets A, B, and C. (a) [6 Points] (A\C) n(C\B) = 0 (b) 17 Points) ( B A) U (C\ A) = (BUC) \ A (c) (7 Points) Suppose that A, B, and C satisfy all these properties: AUBCC. (AUC), B = C. and (AnCUB CA. Prove that A = B