1. Let A and B be sets. Prove A ⊆ B iff p (A) ⊆ p (B). 2. (a) Prove: If | S | ≤ | T |, then |p ( S ) | ≤ |p (T ) |. (b) Prove: If | S | = | T |, then |p ( S ) | = |p (T ) |. 3. Is it possible for p...

1. Let A and B be sets. Prove A ⊆ B iff p (A) ⊆ p (B).

2. (a) Prove: If | S | ≤ | T |, then |p ( S ) | ≤ |p (T ) |.

(b) Prove: If | S | = | T |, then |p ( S ) | = |p (T ) |.

3. Is it possible for p (S) = ∅ for some set S? If yes, what can you say about S? If no, explain why.