Answer
a)Not a function
b)is a function
c)Not a function
Work Step by Step
a) This is not a function, because there may be no zero bit in S, or there may be more than one zero bit in S. Thus there may be no value for f (S) or more than one. In either case this violates the definition of a function, since f(S) must have a unique value.
b) This is a function from the set of bit strings to the set of integers, since the number of 1 bits is always a clearly defined non negative integer.
c) This definition does not tell what to do with a non empty string consisting of all 0's. Thus, for example, f(000) is undefined. Therefore this is not a function.
