1. Let S, be the set of all strings that form base 4 expansions of positive integers. (a) Write a recursive definition for Se: Basis Step: Recursive Step: (b) Consider the function fa : S4 +z+ that takes a base 4 string u and returns the value of u as a positive integer. Describe the function fa using a recursive definition. (c) Consider the function pu: Si + {0,1}* that takes a base 4 string u and returns the binary expansion of u. Describe the function pa using a recursive definition