- #1
Daveyboy
- 57
- 0
f:X\rightarrowY, A\subsetX
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)...
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:
