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Proving a known proof involving injection.

  1. Sep 2, 2012 #1
    trying to learn how to do proofs. So I have A=> B which is injective and E [itex]\subseteq[/itex] B then prove f^-1(f(E)) = E.
    So let x [itex]\in[/itex] f^-1(f(E)) => thus f(x) [itex]\in[/itex] f(E) => x[itex]\in[/itex] E

    So I have proved that x is a point within E, a subset of A, to me I think I am missing something and have not proved f^-1(f(E)) = E.

    any suggestions?
  2. jcsd
  3. Sep 2, 2012 #2


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    Science Advisor

    You need to do a similar argument in the opposite direction. Take x in E and show

    it is in f-1f(E). You have then showed, for the two sets:

    E is contained in f-1f(E).


    f-1f(E) is contained in E.

    This is the standard way of showing equality of sets.
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