1. Consider the following DFA. b Define the function 8:0*=Q completely by specifying the output for each input in ex, e.g., for the input (2,a), 8 (2, a) =3 and for the input (2,b), 8 (2,b)=2. 2. This problem refers to the above DFA and the function d in problem 1. a) Use the function S*: Q*I*> defined in the lectures to show, step by step, how 6* consumes the string aaab symbol by symbol to yield the final state. b) Show, step by step, how 8t consumes the string aaba symbol by symbol to yield a non-final state