1. (10 points) The nonnegative powers of a string w are defined recursively as 0 wi+1 = wi o w for i>0 Given a language L, consider the operation Power(L)-f"| w EL and n 2 0) a. For = {0, 1} and L = {0n1 | n > 0), give an example of a string that is in L* but not in Power(L) and justify your example (Therefore, we can conclude that L* does equality ever hold?) Power(L) is not always true. As an aside (not for credit), b. Let E be an enumerator that enumerates an infinite language L. Consider the high-level descriptiorn of an enumerator E'. E'-- "Ignore the input: 1. For i- 1,2,3..., repeat the following 2. Run E until it prints i strings (recording those strings) 3. For each string x in this collection of i strings: 4. Print , x,22,2, ,x. 23 True or False: L(B) Power (L). Briefly justify your