(a) Compute f(4), f(7), and f (10). Show that computed number is even (use the definition of even). Note: These examples do not prove our claim, but working with small examples can help us to check that a claim is reasonable, before we proceed with an abstract investigation. (b) Use multiplication to check that 15n- + 11n + 2 = (3n + 1) (5n + 2). (c) We will now show that if n is even, then 15n2 + 1In + 2 is even, practicing using rules of inference. (i) Show that if 5n + 2 is even, then 15n2 + 1In + 2 is even. Note: You should interpret this as the quantified statement Vn(5n + 2 is even) -> (15n- + 11n + 2) is even). Your goal is to use universal generalization, so you do not get to work with any specific value of n. It is sufficient to work with the fact that 5n + 2 = 2k for some k, together with the factorization from (a)