For set {a, b, c}, find equivalence relations

Question

Why can't {(a,a)} be an equivalence relation for the set {a,b,c}?

{(a,a)} is reflexive, symmetric, and transitive.

Answer 1

It's not reflexive because it doesn't contain (b,b) and (c,c)

Answer 2

It's not reflexive unless it contains $(x,x)$ for all $x \in\{a,b,c\}$. It doesn't contain either $(b,b)$ or $(c,c)$ so it's not reflexive.