1. Reflexive: a~a.
2. Symmetric: if a~b then b~a.
3. Transitive: if a~b and b~c, then a~c.
Equality and set membership are the most basic equivalence relations, which is why they are often called trivial equivalence relations. Every equivalence relation is constructed from irreducible equivalences.
Equivalence relations are the mathematical foundation for forming quotients.