Prove tha validity of the formula

Question

I came across this question in my assignment:

For each of the following formulas, either prove that it is valid or give a counterexample to its validity.

(a) ((∃xP(x)) ⊃ Q(a)) ⊃ (∀x(P(x) ⊃ Q(a)))

(b) [∀x(P(x) ⊃ Q(a))] ⊃ [∃x(P(x)) ⊃ Q(a)]

I'm assuming that the first formula is not valid while the other one is valid. But how do I prove it and what kind of counterexample do I provide in order to show that a formula is not valid?

Thank you in advance.

Answer 1

Both formulae are valid; thus, you cannot find counter-examples.

For the proof, see Herbert Enderton, A Mathematical Introduction to Logic (2nd - 2001) , page 122.