1. (a) Show that (xP(x) xQ(x)) x(P(x) Q(x)) is not universally valid.

(b) Use rules of inference of Propositional and Predicate Logics to show that if x(P(x) (Q(x) S(x))) and x(P(x) R(x)) are true, then x(R(x) S(x)) is true, where the domain for all quantifiers is the same.

Equivalence statements to prove

EDIT: Discrete Math Question