Let S be the set of all strings in 0's and 1's, and define a function F : S Z nonneg as follows: for all strings s in S, F(s) = the number of 1's in s. (a) What is F(001000)? F(111001)? F(10101)? F(0100)? (b) Is F one-to-one? Prove or give a counterexample. (c) Is F onto? Prove or give a counterexample. (d) Is F a one-to-one correspondence? If so, find F 1