1. The problem statement, all variables and given/known data Let X be a set. Suppose that f is a bijection from p(X) to p(X) such that [itex]f(A)\subseteq f(B)[/itex] iff [itex]A\subseteq B[/itex] for all subsets A,B of X. Show that there is a bijection g from X to X such that for all [itex] A\subseteq X [/itex] one has f(A)=g(A). 2. Relevant equations p(X) is the power set of X. 3. The attempt at a solution This seems too elementary and I doubt that there is something to prove. Can't I just take f=g?