For the alphabet A={0,1}, define the set S = {all strings over A formed by concatenating 1 or more copies of 0111 or 1101} Use mathematical induction to prove (base case and inductive case) that for every positive integer n, if a string s in S has length 4n, then the number of 1's in s is a multiple of 3. State what you are going to prove in symbolic form such as nD, P(n).