Let swap : {a, b} {a, b} be the function that exchanges the as and bs in a string. For example, swap(baaba) = abbab and swap(aaaa) = bbbb.

For L, a language over {a, b}, define swap(L) as follows: swap(L) = {swap(w) | w L}.

(a) Suppose A = {, b, aabb, babababb}. What is swap(A)?

(b) You will now show that the class of regular languages over {a, b} is closed under the swap operator. Let M = (Q,{a,b},,q0,F) be a DFA. Define DFA M such that L(M) = swap(L(M)). You do not need to argue correctness of M; just define it.