Determine whether each argument is valid. If the argument is valid, give a proof using the laws of logic. If the argument is invalid, give values for the predicates P and Q over the domain {a, b} that demonstrate the argument is invalid.

(a)

x (P(x) Q(x)) x Q(x) x P(x)

(b)

x Q(x) x P(x) x (P(x) Q(x))

(c)

x (P(x) Q(x)) x Q(x) x P(x)

(d)

x (P(x) Q(x)) x Q(x) x P(x)

I think a, b, and c are all true. D is false. Can someone help explain why/give proof? Thanks