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Proving the graph of a composite function

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Let f : A → B, g : B → C be functions where A,B,C are sets. ConsiderΓf ⊂A×B,the graph of f,Γg ⊂B×C,the graph of g. Now consider the sets Γ f ×C ⊂ A×B×C and A×Γg ⊂A×B×C. LetΓ=θ(Γf ×C∩A×Γg)⊂A×C where θ : A×B×C → A×C is the projection defined as θ((a,b,c))=(a,c). Show that Γ is the graph of g◦f.
    2. Relevant equations

    3. The attempt at a solution

    I think that I should find a way to show that the first projection of gamma is a bijection. But i dont know how I can do that.
  2. jcsd
  3. Oct 23, 2011 #2
    please help ive been trying for so long
  4. Oct 24, 2011 #3


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    Science Advisor

    Then show us what you have been doing all that time!
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