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About composite mapping

  1. Mar 9, 2008 #1
    Could anybody help me check whether my judgements ture or false? (MJ = My Judgement)

    Suppose f maps A into B, and g maps B into C

    1. If f and g are injective, then g[tex]\circ[/tex]f is injective;
    (MJ)but that when g[tex]\circ [/tex]f is injective, the injectivity of f and g are unsure.

    2. If f and g are surjective, then g[tex]\circ[/tex]f is surjective;
    (MJ)and that when g[tex]\circ[/tex]f is surjective, f and g are both surjective.

    Thx!
     
    Last edited: Mar 9, 2008
  2. jcsd
  3. Mar 9, 2008 #2

    HallsofIvy

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    What reasons do you have for those judgements? Can you think up a simple example where f and g are not injective but g[itex]\circ[/itex]f is? Try the case where A, B, and C have only a few members.
     
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