Give an example to show that the equality in Exercise 14 may not hold if f is not 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 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 38, both in Section 2.3.
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