7) (8 points) Determine whether (q ^ (pq))p is a tautology using logical equivalences. Do not use a truth table. 8) (6 points) How many of the disjunctions pV-q, -p V q, q Vr, q V-r, and q Vr can be made simultaneously true by an assignment of truth-values to p, q, and r? Justify your answer. 9) (8 points) Determine, with justification, whether each of these compound propositions is satisfiable. a) (pvqv-r) A (pvq vs) A (pvr vs) A (p Vq vs) A (pvq vs) b) (p vqvr) A (pvq vs) A (pvq vs) A (p vr vs) A (pvq vr) A (p vr vs)