1. Prove that the empty set is unique. That is, suppose that A and B are empty sets and prove that A = B. 2. Prove: If U = A ∪ B and A ∩ B = ∅, then A = U \B. 3. Prove: A ∩ B and A \B are disjoint and...

1. Prove that the empty set is unique. That is, suppose that A and B are empty sets and prove that A = B.

2. Prove: If U = A ∪ B and A ∩ B = ∅, then A = U \B.

3. Prove: A ∩ B and A \B are disjoint and A = (A ∩ B) ∪ (A \B).

4. Prove or give a counterexample: A \(A \B) = B \(B \A).