Answer this truth table related question for logic and algorithm as soon as possible. (Type v for logical or, ^ for logical and, - for logical not, -> for implication, <-> for biconditional.)

1. Prove that (p(pq)) and pq are logically equivalent by applying the laws of propositional logic.

2. Prove that r(rp) is a tautology by applying the laws of propositional logic.

3. Prove that (pq)(pq) and p are logically equivalent by applying the laws of propositional logic.