2.(Number of states) Let = {a, b}. For each k 1, let C_k be the language consisting of all strings that contain an a exactly k places from the right-hand end. Thus C_k = ^*a^k-1 .

(b) If a DFA enters different states after reading two different input strings xz and yz with the same suffix z then the DFA must enter different states after reading input strings x and y. Explain why.