(This exercise is about writing things formally - it is not difficult once you have cut through the formalism. In short, don't panic - you can do it!) (A) Let M - (Q, sigma, delta, s, A) be a DFA. A state q elementof Q is bad, if for all strings w elementof sigma* we have that delta*(q, w) NotElement A. Let B(M) Subsetequalto Q be the set of bad states of M. Consider the DFA M' - (Q, elementof, delta s, B(M)). What is the language L(M')? Prove formally your answer! (B) Prove that if x elementof: L(M') and y elementof sigma*, then xy elementof L(M'). (C) Let L_1 and L_2 be two regular languages over sigma accepted by DFAs M_1 = (Q_1, sigma, delta_1, s_1, A_1), and M_2 - (Q_2, sigma, delta_2, S_2, A_2), respectively. Describe a DFA M = (Q, sigma, delta, s, A) in terms of M_1 and M_2 that accepts L = {w | w element L_2 and no prefix of w is in L_1} Formally specify the components Q, delta, s, and A for M in terms of the components of M_1 and M_2