This is a question about inductively defined functions and proof by structural induction. I WILL DEFINITELY GIVE YOU A POSITIVE RATING if your answer works. Appreciate your help!

note: the definition of sigma star is given as follows:

(a) Inductively define a function prepend y x y that prepends a character to a string. For example, prependla,ebode) should be eabode (the is explicit in this example only to emphasize the inductive construction of strings). (b) Let 8 be the extended transition function for a DFA. Prove inductively that for all ac E g, pre pena, a