2. For each of the following logical equivalences state whether it is valid or invalid. If invalid then give a counterexample (e.g., based on a truth table). If valid then give an algebraic proof using logical equivalences from Tables 6, 7, and 8 from Section 1.3 of textbook. (a) p (q r) = q (-p v r) (b) (p r) ^ (q r) = ((p^q) r) (c) (p q) ^ (p r) = (p (q^r)) (d) ((pv q) ^ (p vr)) = (q v r)