Discrete math

QUESTION 5 15 MARKS Let a machine M = ({50, 51, 52, 53, 54}, {m, a, e},50, f:. {S2, se}) be the Deterministic Finite Automaton (DFA) with state transition defined as follows (Table 2): Table 2 Next state Input State so Si So S2 51 S1 S2 S1 S2 $2 S3 54 53 $3 S1 S4 54 Si 53 S1 a) a) Draw the state transition diagram for machine, M. (5 marks) b) Determine the final state for the input string mamee. You must show the sequence of state transition. (2 marks) c) Is the input string mamee accepted by the DFA? Justify your answer. (2 marks) d) Find ONE input strings that follow the given conditions and must accepted by machine M. (6 marks) i. Length of strings is 5 and do not contains input m. ii. Length of strings is 6 and do not contains input e. 111. Length of strings is at least 2, start and end with the same input (for example: mam) You must show the sequence of state transition in each