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1. Consider the following DFA. a 2 3 b Define the function 8:9**Q completely by specifying the output for each input in Qx, 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 sin problem 1. a) Use the function S*: Q**> defined in the lectures to show, step by step, how 8* consumes the string aaab symbol by symbol to yield the final state. b) Show, step by step, how * consumes the string aaba symbol by symbol to yield a non-final state