Consider the following sets of integer numbers: S_1 = {4, 5, 6} S_2 = {i: i is even} S_3 = {i: i is divisible by 3} For each set below determine whether it is finite or infinite: S_4 = S_1 times S_1 S_5 = 2^S_1 S_6 = S_1 intersection S_2 S_7 = S_2 intersection S_3 Prove that, if S_1 S_2, then S_2^- S_1^-. Prove the following equalities: (a) Sigma^n_k = 1 (k + 3) = n^2/2 + 7/2 n (b) 1 + x + x^2 + x^3 + ellipsis + x^n = x^n + 1 - 1/x - 1, where x notequalto 1