(a) Give a state diagram for a DFA for the language w E 10, 1 w's second character is a 1) (b) Give a state diagram for a DFA for the language {w {0, 1} | w's last character is a 1} (c) Use the method described in class to construct a DFA which recognizes their intersection. (d) Minimize it and prove that your DFA has a minimal number of states. (You just need to show the proof that it is minimal, not the steps in the minimization.)