Provide three proofs of the logical equivalence P Q = (P^Q) V (¬P ^ ¬Q): (a) Prove the logical equivalence using a truth table. (b) Prove the logical equivalence using a symbolic argument. [HINT: Start with the right-hand side (PAQ) V (PA-Q) and expand it using two applications of the Distributive Laws.] (c) Prove the logical equivalence using an explanation in words.

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