Introduction to Logic
Consider a language with a single object constant a, a single unary function constant s, and two unary relation constants p and q. We start with the premises shown below. We know that p is true of s(a) and only s(a). We know that q is also true of s(a), but we do not know whether it is true of anything else.
Prove ∀x.(p(x) ⇒ q(x)). Hint: Break the problem into two parts - first prove the result for s(x), and then use that intermediate conclusion to prove the overall result.