1. [25 points] Let ={0,1}. The reverse of a string x denoted by rev(x) and is defined by the following recursive rule: - rev(c)=c - x,a,rev(xa)=arev(x) For any set A, define rev(A) to be: rev(A)={rev(x):xA} Can we always (i.e., for any A) say that if A is regular then so is rev (x) ? Prove your answer. [hint: if your answer is yes, then you can give a DFA M for rev(x) based on the DFA for A, and then show that L(M)=rev(x). If your answer is no, you can find a specific A and show that rev (x) is not regular, e.g., using pumping lemma]