Let S be the set of binary strings defined recursively as follows: Basis step: 1 elementof S Recursive step: If x elementof S then xx elementof S and 0r0 elementof S (If x and y are binary strings then ay is the concatenation of x and y. For instance, if x = 0111 and y = 101 then xy = 0111101.) (a) List the elements of S produced by the first 2 applications of the recursive definition. Find S_0, S_1 and S_. (b) Use Structural induction to prove that every element of S has even number of 0's in it