Set theory, functions, bijectivity

1. Sep 5, 2009

Daveyboy

f:X$$\rightarrow$$Y, A$$\subset$$X
f(Ac)=[f(A)]c implies f bijective.

Just trying to apply the definitions of injective and bijective. The equivalence makes sense but I am having a hard time showing it.

f(x)=f(y) implies x=y and for every y in Y there exists a x in X s.t. f(x)=y.

I mean all I have is if f(x)=f(y)
then f(X\x)=Y\f(x\x)=f(X\y)-Y-f(X\y)...

Last edited: Sep 5, 2009
2. Sep 6, 2009

latentcorpse

what's the question?

3. Sep 8, 2009

Daveyboy

this implication