equivalence relation

a binary relation is an equivalence relation if

• \(R\) is reflexive: \(xRx\) is true for all \(x\)
• \(R\) is symmetric: \(x R y\) is true implies \(y R x\) is true
• \(R\) is transitive: for every \(x,y,z\), \(xRy\) and \(y R z\) implies \(x R z\)