2. For each of the following logical equivalences state whether it is valid or invalid. If...

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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) 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)