4. Show that Pn(P Q)-P^ Q are logically equivalent using truth tables, and also by using the laws of propositional logic 5. Show that -PV(-PQ) A P is a tautology. 6. Show that (P Q) ^-P ^ Q) is a contradiction. 7. Let P(z) ="z has come", Q(x)-"the north likes r". The universe of z is seasons. Rewrite the following predicates in words: (b) (P() AQ(x)) V P(x) 8. Let P(z) ="z is cold", Q(x,y) ="z is y". The universe of x is seasons, and the universe of y is f"coming", "going"]. Rewrite the following predicates symbolically: (a) "Winter is cold, and winter is coming (b) "If winter is coming, then summer is going