3. (8 points) (a) Give a recursive definition of the function zeros(s), which counts the number of zeros in a bit string s to, 1 Hint: the domain of this function is [0, 1)* and its codomain is the set of nonnegative integers N. For ezample, zeros(1101)1 and zeros(0010) 3. (b) Use structural induction to prove that zeros(st)-zeros(s) +zerost) Your proof will need to use the definition you came up with in part (a) Note that st refers to the concatenation of the strings s and t; on the RHS the + is addition of integers. Hint: you may find the recursive definition of string concatenation, Definition 2 on page 350, useful