Question: 1. How does |Fn| compare to |Pn|.
2. Forget the previous question. Instead, prove that F is a bijection; recall that this means you have to show that F is one-to-one and onto.
3. Explain how this gives yet another proof of Theorem.
Theorem: A set with n elements has 2n subsets.
It is useful to have different proofs of the same theorem because they give different understandings of, or different perspectives on, the mathematics involved. Hidden in the above proofs is the following.