Above is the question I wanted to be solved

And for those questions, A1, A2, and A3 are

2. (30 point) By using the DFAs you have constructed in the first question, apply the Cartesian construc- tion to design a DFA D1 and a DFA Du such that L(D)-Ai A2 and L(Du) Al UA3. 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 3. (40 point) By using the DFAs you have constructed in the first question, design the DFA's Dr and Dy such that L(D- - A2 and L(Dy)- A2 A 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. (a) A1- [ (b) A2 = {w | the length (c) A3 {w laba is a substring of w} w w has an even number of a's ). of w is 3r +1 for some r -0) Here, qo is the initial state and q2 the final state, state transitions are given below 1 42 A2 Here, qo is the initial state and q1 the final state, state transitions are given below: a,b a,b ah 42 a, b Here, qo is the initial state and q3 the final state, state transitions are given below: a,b do Ch 42 43