Ex.2.2.7 (the same in the second edition of HMU). Q3 [10 pts] P.54 For your convenience, the question is also repeated here: Let A be a DFA and q a particular state of A, such that delta(q,a) on the length of the input that for all input strings w, delta^hat(q,w) = q. Here, delta denote the transition function of A and delta^hat denotes the extended transition function. = q for all input symbols a. Prove by induction