5. (7 points) Prove (pA (pq))q is a tautology using logical equivalences (laws). Identify the logical equivalence(s) used in each step. Complete the proof below by filling in the blanks. (pA (pq))q(p ^ (pq)) V q (p V(pq)) Vq (p V(p V q)) V q (p V (pAq)) Vq (pVp) A (p V q)) Vq ((pvp) A (p V q)) Vq (TA (p Vq)) Vq (p Vq) V q p V (q Vq) p V (q Vq) p VT < >T Implication Law (1) Implication Law De Morgan's Law (2) Commutative Law Negation Law Identity Law Associative Law Commutative Law Negation Law Domination Law