4. (20 points) Consider the following set defined recursively over 9 = {a,b}. Write S, as a regular set. (16 points). Explain your answer. (4 points) (i) Basis: A E S (ii) Recursive step: If we Sy, then aaw e S, and wbb S. (iii) Closure: S, consists of exactly the elements that can be obtained by starting with the basis elements of S, and applying the recursive step a finite number of times to construct the new elements of S