2. DFA Design and Analysis (a) Design a DFA M with at most 4 states for the language L = {W E {0,1}* w contains at least one 0 and w is even }. Present your DFA in the form of a state diagram and include a brief rationale for its design. (b) Prove that your DFA M of part (a) accepts the language L, i.e. prove that L(M) = L