# Proving power set generation is NP-Hard?

Suppose I have two sets $$A$$ and $$B$$ containing integers. Let $$B’$$ be the power set of $$B$$. Then suppose I have an algorithm that enumerates all possible pairings of elements in $$A$$ and $$B’$$ to apply a function $$f$$ to them and check something. How can I prove this algorithm is NP-Hard?