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 (P(x) ∨ Q(x)) ∴ ∀x Q(x) ∨ ∀x P(x)