Use induction over the size of strings to prove that the following NFA over the alphabet sigma = {a, b} recognizes the regular language sigma*ab (that is, it accepts all w sigma* that end with ab). For all strings w E* there exists a computational path that terminates in the state q_1 (terminates without "dying" in the middle of computation process). For all strings w E*a (i.e., all strings that end with an a) there exists a computational path that terminates in the state q_2. For all strings w sigma*ab there exists a computational path that terminates in the state q_3. Note that due to item (3) this statement implies that the language of the above NFA is sigma*ab. In the base case you need to show that the statements holds for strings of size 0 and 1. As for the induction step, you need to show that the above induction hypothesis holds for all strings of size n greaterthanorequalto 2, assuming that it holds for all strings of size smaller than n. To do that for any string w of size n greaterthanorequalto 2 you can consider three cases: w sigma*a, w sigma*ab, and w sigma* bb. Note, for example, that if w belongs to sigma*a, it also belongs to sigma*; therefore, as suggested by the statement, you need to show that there exists a computational path on w that terminates in q_1, and there also exists another computational path on w that terminates in q_2