Proof about relations

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Homework Statement


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.

Homework Equations




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?
 

Answers and Replies

  • #2
fresh_42
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I wonder why there's only reflexive needed. But seems ok.
 

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