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bedi
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Homework Statement
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).
Homework Equations
p(X) is the power set of X.
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?