Prove by induction that for any string w that belongs to L, na(w)= nb(w), where nc(w) is the number of characters c in w.

. Consider L={w na(w) = nb(w)}. Now consider the following inductive way to generate elements of L Basis: e is in the language Recursion 1: If the string w is in the language, then so are awb and bwa Recursion 2: If the strings w and v are in the language, so is wy. . Consider L={w na(w) = nb(w)}. Now consider the following inductive way to generate elements of L Basis: e is in the language Recursion 1: If the string w is in the language, then so are awb and bwa Recursion 2: If the strings w and v are in the language, so is wy