2. (10 points) Let B be the DFA given by the following transition dia- gram: start 0 Prove that L(B) is the language of all binary strings that end with an odd number of ls. Hint: Use weak induction on the length of the input string, and let P(n) be the statement that, for all input strings w with (w = n, the following conditions hold: a. If 8* (90, w) = qo, then w is or ends with 0. b. If 8* (90, w) = 91, then w ends with an odd number of 1s. c. If 8* (90,w) = 92, then w ends with an even number of ls