2. Regular languages are context-free Formally prove that every regular language is context-free. Use the following ingredients in your proof: the recursive definition of regular expressions; the fact that L is a regular language if and only if L = L(e) for some regular expression e; induction on the length of a regular expression recall that every regular expression is a string of length at least 1 consisting of elements in as well as the symbols U, *, (, ),e,0; the fact that context-free languages are closed under the regular operations; that is, if Li and L2 are context-free languages, then L1 UL2, LL2 and L are context-free. (You may use this result without proof.)