I have been busy working on this problem and I was wondering if anyone could give me some help...

Q: Determine and justify for each of the following cases whether f is a function from S to I, where S is the set of all bit strings, and I is the set of all integers.

*For these bit strings would be as follows {1,3,5} = 10101

1.) F(s) is the position of a 0 bit in string s
2.) F(s) is the number of 1 bits in string s
3.) F(s) is the smallest integer i such that the ith bit of string s is 1, and F(s) = 0 when s is the empyt string, a string with no bits