Let P and Q be arbitrary sentences. Taking H = {PVQ, ~P) as the set of hypotheses, formally prove Q. (If you invoke any tautologies, give their truth tables.) Let P and Q be arbitrary sentences. Taking H= {P, Q} as the set of hypotheses, formally prove PAQ. (Hint: begin by showing that P (Q PAQ) is a tautology.) Let P and Q be arbitrary sentences. Taking H = {PAQ) as the set of hypotheses, formally prove P. (If you invoke any tautologies, give their truth tables.) Let P and Q be arbitrary sentences. Taking H = {P) as the set of hypotheses, formally prove PV Q. (If you invoke any tautologies, give their truth tables.)