1. The problem statement, all variables and given/known data Let A be the set of all sets. #1.) Show that P(A) is a subset of A. #2.) Find a contradiction. 2. Relevant equations 3. The attempt at a solution #1.) We know that P(A) is a set. Therefore it must be in A, since A is the set of ALL sets. #2.) I cannot figure out what to do here. I do not have a theorem that says that |P(A)| > |A|. I do have a theorem that states that there is no injection from P(A) to A and also that there is no surjection from A to P(A). Since there is no injection from P(A) to A, does this alone mean that |P(A)| > |A| ?