Consider the alphabet -a, b). Let I be a set whose elements are strings over . Define L recursively by the following: 2. Base Case: E L a represents the empty string) Recursion Rule: If E and w E L, then xaw E L. a. Apply the recursion rule three times to build the first 3 (or 4 if you count the base case) "stages" of the construction of the set L. Stage 0:(a) Stage 1: Stage 2: Stage 3: b. State a non-recursive definition for this set. (You can describe it in words.) c. Are the following strings in the set L? For each string circle "Y" or "N". aaababaa YN babaabaa Y N babaaaba Y N aababaa Y N