Given a language A C 3*, we write A1 to denote the set of left halves of words in A. That is 2 A = = { * | Fy(y * and [2] = ly and xy E A)} For example, if A = {e, a, ba, aba, aabb}, then A1 = = {e, b, aa} 2 Prove that if A is regular, then A1 is also regular. 2 [To do so, assume that A is accepted by some DFA M (Q, 8, 8, s, F) and construct a DFA (or NFA) M' = (Q', 2,8', s', F') that accepts Az. Specify all components of M' and explain what it does.]