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Proof about relations

  1. May 19, 2016 #1
    1. The problem statement, all variables and given/known data
    Let X be a set and R ⊂ X × X. Assume R is an equivalence relation and a function. Prove that R = I_X, the identity function.

    2. Relevant equations


    3. The attempt at a solution
    Proof

    We know that R has to be reflexive, so for all elements b in X, bRb but b can't be related to any other element because of the definition of function, so b is just related to b. It's easy to see that the relation is equivalent. Therefore, R=I_x because R assigns to each element x in X, the element x in X.

    How does that look?
     
  2. jcsd
  3. May 19, 2016 #2

    fresh_42

    Staff: Mentor

    I wonder why there's only reflexive needed. But seems ok.
     
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