Equivalence relations on the set [3].

Question

Consider the set $[3]$ and the equivalence relation defined by the graph: $$\{(1,1), (1,2), (2,1), (2,2), (3,3)\}.$$ I know this is an equivalence relation because it is symmetric, transitive, and reflexive. My professor says $1\sim 2$ since $\sim$ is reflexive, symmetric and transitive, but $1$ is not equivalent to $3$? Why is this the case?

Answer 1

If $1$ were equivalent to $3$, then $(1,3)$ would be in $R$. Since $(1,3) \not \in R$, $1 \not \sim 3$. The equivalence of elements when you know all ordered pairs $(x,y) \in R$ is not going to be something you attempt to draw out from the properties of equivalence relations; it'll be quite clear since you'll know outright whether they're related or not.

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Mostly posting this so this question can be finally considered to have an answer and thus be removed from the unanswered queue. Made it Community Wiki since I have nothing much of substance to add.