9. (10 points, Extra Credit) Mind Your Languages. Consider a mapping o of every symbol of an alphabet a Eto a language o(a) = L over an alphabet I (note that and I may or may not be the same). We then extend the mapping o from strings over to languages over I as follows: o(s) = {{}, and o(wa) = (w)o(a) for we * and a E. Finally, we extend the mapping o from languages over Eto languages over I as follows: if L CE*, we define o(L) = UWEL 0(w). Show that if L is a CFL and o is a mapping such that o(a) is a CFL for every symbol a E, then 0(L) is also a CFL. 9. (10 points, Extra Credit) Mind Your Languages. Consider a mapping o of every symbol of an alphabet a Eto a language o(a) = L over an alphabet I (note that and I may or may not be the same). We then extend the mapping o from strings over to languages over I as follows: o(s) = {{}, and o(wa) = (w)o(a) for we * and a E. Finally, we extend the mapping o from languages over Eto languages over I as follows: if L CE*, we define o(L) = UWEL 0(w). Show that if L is a CFL and o is a mapping such that o(a) is a CFL for every symbol a E, then 0(L) is also a CFL