Question: Let f: AB be a function from a set A to a set B. Let := P(f):P(A) P(B) be the function on power sets which

Let f: AB be a function from a set A to a set B. Let:= P(f):P(A) P(B) be the function on power sets which sends SA to f[S]B. Also, let':P(B)P(A) be the function which sends TB to f^-1[T]A. Show thato': P(B)P(B) is the identity function on P(B) if and only if f is a surjection.

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