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Proving the graph of an inverse function

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data
    Let f:A→B be a bijection and let f-1 :B→Aitsinverse. If Γ ⊂ A×B is the graph of f, show that the set, Γ′ ⊂ B×A defined as Γ′ = {(b, a)|(a, b) ∈ Γ} is the graph of f−1.

    2. Relevant equations



    3. The attempt at a solution
    So far i have proved that the second projection of gamma must be a bijection. I know that i need to somehow show that the first projection of gamma prime is a bijection, but im not sure how to do that.
     
  2. jcsd
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