(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that f : X ! Y is 1-1 and onto if and only if for each set A [itex]\subset[/itex] X, f(A^c) = [f(A)]^c. ......c is a complement ....

2. Relevant equations

proof by contradiction.

if f is not 1-1,there are x and y with f(x)=f(y)

3. The attempt at a solution

I was thinking if f is not onto ...then i can say A=X...BUT i can't figure it out..i can explain one to one or onto..i am just having hard time here.

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# One to one and onto

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