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Injective function

  1. Dec 22, 2009 #1
    who can help me?
    ı want to prove this
    If f : X → Y is injective and A is a subset of X, then f −1(f(A)) = A.
    but how can I do this :(
     
  2. jcsd
  3. Dec 23, 2009 #2

    CompuChip

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    So being injective means that whenever f(a) = f(b) in Y, then a = b in X.

    The usual proof for such statements is to show two inclusions. Let's start with [itex]f^{-1}(f(A)) \subseteq A[/itex].
    Let x be an element of the set on the left hand side. So x is an element in X, for which [itex]x \in f^{-1}(f(A))[/itex]. Can you show that x should in fact be an element of A?
     
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