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Set theory, functions, bijectivity

  1. Sep 5, 2009 #1
    f:X[tex]\rightarrow[/tex]Y, A[tex]\subset[/tex]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. jcsd
  3. Sep 6, 2009 #2
    what's the question?
  4. Sep 8, 2009 #3
    this implication
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