Given a word w in an alphabet = {a,b}, define the swap of w, denoted w, to be the word obtained by swapping a's and b's appearing in w. That is, if w = W1W2 ...Wn-1Wn, then we = V1 V2 ...Un-1 Un, where vi = a if wi b and vi = b if wi = a. Further define the swap of a language L, denoted L, to be the set of all swaps of words in L. That is LS = {WS : WE L}. (a) Give a constructive proof using finite automata to show that the set of regular languages is closed under the operation of swapping (In other words show that if L is regular, then I is also regular by constructing a machine M such that the language of M is LS.) (b) Give a constructive proof using regular expressions to show that the set of regular languages is closed under the operation of swapping. (In other words show that if L is regular, then LS is also regular by constructing a regular expression for the language LS.)