Let be an alphabet, and let x where |x|=n. Recall that x R =x[n]x[n1]...x[1] is the reverse of x. Let A. Define the reverse of A as A R ={xR |xA}.Prove that the 2 class of regular languages is closed under the reverse operation, i.e., prove that if A is regular, then AR is regular. Do this by showing how to convert a DFA D into an NFA N such that L(N) = L(D)R. Hint: N should simulate running D backwards: guess an accept state that D could end up in, and when reading a symbol b , guess what state(s) D could have been in prior to reading b. With proper guessing on a string in L(D)R, N should end up back at the start state of D.