Given a word w in an alphabet ? = {a,b}, define the swap of w, denoted wS, to be the word obtained by swapping a's and b's appearing in w. That is, if w = wiW2 ... Wn-1Wn, then wS = V1 V2 ... Un-1 Un, where vi = a if Wi 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}. b and vi (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.)