Prove or disprove: For every nonempty set A, there exists an injective function f: A -> P(A).

So this is saying that for this function f, every element of A has an image in the power set of A, right? But not every element of the power set has to be defined by f(A), right?

I think this could be proven but honestly i cannot think of a way to go about doing it. Please help and if you have a strategy please explain where you got it/how you came up with it so I can better understand the problem. Thanks so much!