Consider the set S1 constructed recursively. The recursive step takes a string w from S1 and concatenates the same symbol to the beginning and end of w. (1) (ii) (it) Basis: € S1, a € S1, and b E S1 Recursive step: if we S1, then awa E S1 and bwb = S1 Closure: S1 consists of exactly the elements that can be obtained by starting with the basis elements of S1 and applying the recursive step finitely many times to construct new elements of $1. Use induction to prove that every string in S1 is a palindrome. A palindrome is a string that reads the same from left to right and from right to left.

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