Let ={a,b,c} and let L={ The sum of the number of b's and the number of c's in is even, and ac is not a substring of }. Design a deterministic automaton M=(Q,,,q0,F) whose language is L. For full marks, your answer should include the following: (a) The set Q of states. (b) The start state (in case you used a name different from q0 for this). (c) The set F of accepting states of your DFA. (d) The transition function :QQ, given by either a transition diagram or a transition table. (e) For each state qQ, a description of the corresponding set Sq such that Sq={w(q0,)=q} (where q0 is assumed, here, to be the start state for your DFA). (f) A proof that your transition function is well-defined and consistent with the sets that you have given above - so that, for every state qQ and for every symbol , S(q,) for every string Sq. (g) A proof that qFSq=L, so that the language of your DFA really is the given language L