Hello, I would like to understand how can we prove these set theory proofs, and how can we find a counterexample and prove it?? Please could you provide assistance with it and while explaining could you show steps on how to prove them?? Thank you

Definition. Let A and B be sets. . The union of A and B is the set AUB = {x : x ( A orxEB}. . The intersection of A and B is the set AnB = {x : x 6 A and x EB}. . The difference of A and B is the set A - B = A\\ B = {x : x E A and x # B}. . Given a set A C X we define the complement of A in X to be X \\A. We write A" for the complement of A when the set X is understood. Puzzles for Practice Let A, B, and C be subsets of X. Determine if the following are true or false. If false, give a counter example. If true, give a proof. It may help you to draw some Venn diagrams to get an idea of why the statement may be true/false. 1. ACAUB 2. If CCAUB, then AnB C C. 3. If AUCC BUC, then A C B. 4. A C B if and only if BC CAC