please answer all questions

a) Let M={S,I,qa,fb,F) be the DFA such that S={q0,q1,q2,q3},I={a,b},F={q1},q2= initial state and fs is given by: fs(q0,a)=q1,fs(q1,a)=q3,fs(q2,a)=q1,fs(q3,a)=q3,fs(q0,b)=q2fs(q1,b)=q2fs(q2,b)=q2fs(q3,b)=q2 i. Construct a state transition diagram of the DF A given the state transition function, fa. (4 marks) ii. DFA can be applied for verification of email password. Justify why DFA is suitable for verification? (1 mark) b) Given a deterministic finite automaton (DFA) as in Figure 8 . i. Construct a state transition table for state transition diagram. (5 marks) ii. Identify whether the following input can be accepted by the DFA. Show the transition of each state for the input given. (6 marks) a. a a a a a b. ab a bab c) Draw a transition diagram that can accept input that contains 101 . (4 marks)