355f2001-assign-001 - A is not in the range oF f . Problem...

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Mth 355 Assignment 1 Fall 2001 Due: Oct 8, 2001 Bent Petersen 355f2001-assign-001.tex Let X be a set. Recall we defne the power set P ( X )o F X as the set oF all subsets oF X , P ( X )= { A | A X } . Recall we saw in class Proposition 1. If X is a nonempty set and f : X P ( X ) then f is not epimorphic (surjective, onto). Proof. Let A = { x X | x/ f ( x ) } . IF A = f ( y )Forsome y X then y A iF and only iF y/ A
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Unformatted text preview: A is not in the range oF f . Problem 1. Use the proposition above together with a grubby argument, or come up with your own elegant argument, to prove the Following proposition. Proposition 2. If X is a nonempty set and f : P ( X ) X then f is not monomorphic (injective, one-to-one)....
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