7. *15 Points] Given a language A CS*, we write A, to denote the set of left halves of words in A. That is A1 = {x S* | 3y(y S* and (x1 = \y and xy e A)} For example, if A = {s, a, ba, aba, aabb}, then A= {s,6, aa}. Prove that if A is regular, then A, is also regular. [To do so, assume that A is accepted by some DFA M = (Q.1,6, s, F) and construct a DFA (or NFA) M' = (0.5,8,8%, F') that accepts Aj. Specify all components of M' and explain what it does