2. (8 marks) (a) (2 marks) Draw the state diagram for a DFA recognizing language L- contains at least three b's. (b) (2 marks) Draw the state diagram for a DFA recognizing language L2 = {x x starts with an a and contains at most one b} (c) (Bonus + 4) Draw the state diagram for a DFA recognizing language L3 = L1 U L2. Hint: One option is to use the construction of Theorem 1.25 in the text. d) (4 muks) Draw taeoizing ln L