Consider the following fact. Suppose AA and BB are sets, that SASA, TATA, and ff is a function mapping ABAB. Then f(ST)f(S)f(T)f(ST)f(S)f(T). Which of the following sets, subsets and definition for the function ff can be used to demonstrate the fact that f(ST)f(ST) might be a proper subset of f(S)f(T)f(S)f(T) ? (Hint: This problem is probably best tackled by actually plugging these sets/subsets into ff and seeing which case demonstrates the proper subset case of the above fact, f(ST)f(S)f(T)f(ST)f(S)f(T))

Select one:

A={1,0,1}A={1,0,1}, B=ZB=Z, S={1,0}S={1,0}, T={0,1}T={0,1}, f(x)=x2f(x)=x2

A={1,0,1}A={1,0,1}, B=ZB=Z, S={1,0}S={1,0}, T={0,1}T={0,1}, f(x)=x3f(x)=x3

A={0,1,2}A={0,1,2}, B=ZB=Z, S={0,1}S={0,1}, T={1,2}T={1,2}, f(x)=x2f(x)=x2

A={1,0,1}A={1,0,1}, B=ZB=Z, S={1,0}S={1,0}, T={0,1}T={0,1}, f(x)=x