I've been racking my brain on this one and I have no idea on where to even start, so any help would be appreciated!
Let A and B be infinite sets with the same cardinality. Prove that P(A) and P(B) have the same cardinality. Do this by giving explicitly a bijective function from P(A) to P(B). You must also prove that your function is indeed a bijection (show that it is 1-1 and onto).