Thoery of Computation - Reversal

Given a language L, we define Rev(L), the reverse of L as {reverse(w), for all w in L} (for example, Rev({"abc", "cb"}) is {"cba", "bc"}). Prove by induction on the structure of regular expressions that if L is regular (meaning, it can be represented by a regular expression), then Rev(L) is also regular.

In your proof, you can make use of the following facts about languages without having to prove them:

Rev(L₁ U L₂) = Rev(L₁) U Rev(L₂)

Rev(L₁ ^o L₂) = Rev(L₂) ^o Rev(L₁)

Rev(L*) = (Rev(L))*

Hint: start by formulating very carefully what exactly is the claim that you will be proving about all regular expressions.