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Proof Help

  1. May 30, 2006 #1
    Hello Members

    I am having a little bit of a problem solving this proof for my Discreet math course.

    If g and f o g are onto(Surjective), is f onto(Surjective)? Need to prove. I belive that f has to be Onto.

    so I have g: A -> B
    f: B -> C

    Well I understand that a function is onto(Surjective) when it maps to all images. So for g all the elements in A map(hit) element in B.

    So f o g: A -> C where every element of C must be map to. I belive that since C is the Image of f that this means that f must be onto(Surjective).

    Can someone give me advise on how to prove this? Or even just some advise in general on proofs.

  2. jcsd
  3. May 30, 2006 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    The image of fg is a subset of the image of f. If f is not surjective then fg cannot possibly be surjective.
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