1. (15 marks): Let {a,b}. Design (and draw a picture of) a deterministic finite automaton M (Q, 8, 8,90, F) for the following language L E*, and explain (briefly) why your DFA is correct: L = {we 2* | w includes two or more a's but at most one b}. Your answer should include a brief description of each set Sq = {w * | ** (40W) =q}