Proving R = I_X: Equivalence Relation and Function Homework Solution

[Danielm]

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?

 

[fresh_42]

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