(30 point) By using the DFAs you have constructed in the first question, apply the Cartesian construction to design a DFA D and a DFA Du such that L(D) A1 n A2 and L(Du) A1 U A3. Your answer should provide, for each DFA, a finite state diagram where all the states, the starting state, all of the accepting states and all the transitions (with the corresponding labels) are displayed/drawn clearly. Show intermediate step(s) when applicable A1- A2 a,b a,b 42 a,b - a,b 2