1. Let A be the DFA you defined in the previous problems, and consider the string w =001011. Confirm that w LA, by showing that *q0, w F where q0 is the start state of A and F is its finish states. You have to show this formally using the inductive definition of * (Start with * q0, 0 and then * q0, 00 and then *q0, 001 and so on...)

2. Each of the following languages is the intersection of two simpler languages. In each part, construct DFAs for the simpler languages, then combine them using the construction of product automaton discussed in class

a. {w|w has at least three as and at least two bs}

b. {w|w has an odd number of as and ends with a b}