Consider this inductive definition for a set of integers S. Base Case: 6 S. Inductive Step: if m is in S and n is in S, then m + n is in S. Let A = {6i |i Z*}. We prove that A = S. (a) [11 Pts] Prove that ACS using mathematical induction. In other words, prove that for alli Z*, 61 S. (i) [3 Pts] First, state what you prove for the base case. Then, prove it. (ii) (iii) i. (b) [11 Pts] Prove that SA using structural induction. In other words, prove that for all. XES, X = 6i for some IE Z*. [3 Pts] First, state what you need to prove for the base case. Then, prove it. ii. [2 Pts] State what you assume and what you prove for the inductive step. iii. [6 Pts] Now, prove the inductive step. [2 Pts] State what you assume and what you need to prove for the inductive step. [6 pts] Now, prove the inductive step.