Let G be a left-linear grammar, and let ^G be the grammar as we defined: ^G has the same terminal and variable sets as those of G. Furthermore, if G has a production rule A -> Aw, then ^G has a production rule A -> w^R A, where w^R is the reverse of the string w. _ Prove that L(^G)) = L^R(G). _ Show that there exists a right-linear grammar for the language L(G). Note 1: You can use the fact that every right-linear grammar produces a regular language, and vise versa,. But you cannot assume the same result for left-linear grammars. This problem asks you to prove it.