Question: Given a word w in an alphabet E, define the reverse of w, denoted wR, to be the word obtained by reversing the order of

Given a word w in an alphabet E, define the reverse

Given a word w in an alphabet E, define the reverse of w, denoted wR, to be the word obtained by reversing the order of the characters appearing in w. That is, if w = W1W2 Wn-1 Wn, then = WnWn-1 ... W2w1. Further define the reverse of a language L, denoted LR, to be the set of all reverses of words in L. That is LR = {WR : WE L}. WR (a) Give a constructive proof using finite automata to show that the set of regular languages is closed under the operation of taking reverses. (b) Give a constructive proof using regular expressions to show that the set of regular languages is closed under the operation of taking reverses

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