For the following definitions, let be a set, .

## Relation

A **relation** on a set is a subset of the *Cartesian Product* .

## Equivalence Relation

An **Equivalence Relation** on a set is a *relation* with the following properties:

**Reflexivity**: for all .**Symmetry**: .**Transitivity**: and .

## Equivalence Class

Let and be an *Equivalence Relation* on , then the subset

is an **Equivalence Class** that is *determined* by . (Note that contains because .)

*Now go lift something heavy,*

Nick Horton