2. In IndivHW3, you showed that the class of regular languages over the alphabet [0,1 is closed under the operation Reverse(L). (a) To prove that the class of context-free languages over the same alphabet is closed under the same operation, would it be enough to use the facts that (1) the class of regular languages is a subset of the class of context-free languages and (2) the class of regular languages is closed under Reverse? Why or why not? (b) To prove that the class of context-free languages over the same alphabet is closed under Reverse directly, consider the context-free grammar G = (V,(0,1), R, S). Define a (new) CFG G' = (V, {0,1), R', S') where v, = R'= S' This will be the set of variables for your new grammar This will be the set of rules in your new grammar This is your new start variable. Make sure you choose an element of V" (by filling in the blanks above) such that L(G')-Reverse L(G)) You do not need to give a formal proof that your construction works, but explain in a sentence or two why you defined the construction in this way. (c) Since CFGs and PDAs are equivalently expressive, we could have approached this problem using PDAs. Would you expect it to be harder or easier to prove the closure of the class of context-free languages under Reversal using PDAs