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Math Help - proving functions onto

  1. #1
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    proving functions onto

    Hey I'm in need of a push in the right direction.
    My problem is:
    Assume A,B,C are arbitrary sets show if f:A -> B is onto and g: B->C is onto then g(f): A->C is onto. (EDIT - meant to say g(f))

    What do I need to show to prove A-C is onto?
    Last edited by del3226; October 27th 2010 at 12:11 PM. Reason: meant to say g(f)
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  2. #2
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    Every point is C has a pre-image in B and that pre-image has itself a pre-image in A.


    If \left( {\forall t \in C} \right)\left( {\exists x_t  \in B} \right)\left[ {g(x_t ) = t} \right]\;\& \,\left( {\exists w_{x_t }\in A } \right)\left[ {f\left( {w_{x_t } } \right) = x_t } \right]

    So g\left( {f\left( {w_{x_t } } \right)} \right) = g\left( {x_t } \right) = t.
    Last edited by Plato; October 27th 2010 at 03:30 PM.
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  3. #3
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    Do you mean, "Show g*f is onto"?

    Suppose y in C.
    Since g is onto, there is an x in B such that g(x) = y.
    Since x in B, and since f is onto, there is a z in A such that f(z) = x.
    So y = g(f(z)).
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  4. #4
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    Thank you both. And yes typed the question poorly.
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