4. Use mathematical induction to prove the following. (a) Prove that n+n is even for any positive integer n. (b) prove that for any integer n 1, if A1, A2, A3, A (A, B)U(A B)UU(A (c) For any positive integer n - = and B are any sets, then B) (A UA UA UUA)-B. 1 + n+1 n+2 1 1 2n 1 1 +...+ =1-+ 2 3 1 1 2n-1 2n (d) Let z be a real number greater than -1. Prove that for all integers n 2. 1+xn (1+x)" (e) Let a 12, a = 29 and a = 50-1-60-2 for all n 2. Prove that an 5.3" +7.2" for all integers n 0