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?