1. Let A and B be sets. Prove that p (A ∩ B) = p (A) ∩ p (B). 2. Let A and B be sets. Prove that p (A) ∪ p (B) ⊆ p (A ∪ B), and show by a counterexample that equality does not hold. 3. Let A and B be...

1. Let A and B be sets. Prove that p (A ∩ B) = p (A) ∩ p (B).

2. Let A and B be sets. Prove that p (A) ∪ p (B) ⊆ p (A ∪ B), and show by a counterexample that equality does not hold.

3. Let A and B be sets. Prove or give a counterexample: p (A\B) = p (A)\p (B).