Suppose that is a function from A to B where A and If are finite sets. Explain why | f(S) | = | S | for all subsets S of A if and only if f is one-to-one.Suppose that f is a function from A to B. We define the function Sf from p(A) to p(B) by the rule Sf(X) = f(X) for each subset X of A. Similarly, we define the function Sf?1 from p(B) to p(A) by the rule Sf?1(Y) = f?1(Y) for each subset Y of B. Here, we are using Definition 4, and the definition of the inverse image of a set found in the preamble to Exercise 42, both in Section 2.3.

SolutionStep 1In this problem, we have to show that function A to B where A and B finite sets.and we have to explain that why f(S) = |S| for all subsets S to A if and only if f is one to one function.