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Let a machine M = ({so, s1, 52, 53, 54), m, a, e), 50, fs, sul) be the Deterministic Finite Automaton (DFA) with state transition defined as follows (Table 2): Table 2 Next state Input e State So 51 So S2 SI SI $2 SI S; S3 SA 53 S 51 ST SI 53 Si b) Draw the state transition diagram for machine, M. (5 marks) Determine the final state for the input string mamee. You must show the sequence of state transition (2 marks) Is the input string mamee accepted by the DFA? Justify your answer (2 marks) c)