Equivalence Relation

A relation between elements of a set \(S\) is an equivalence relation if it is

1. Reflexive: \(\forall x\in S (x\sim x)\);
2. Symmetric: \(\forall x, y\in S (x\sim y \rightarrow y \sim x)\);
3. Transitive: \(\forall x, y, z\in S (x\sim y \land y\sim z \rightarrow x\sim z)\)