## Equivalence relation |

in

, anmathematics **equivalence relation**is a that isbinary relation ,reflexive andsymmetric . the relation "is equal to" is the canonical example of an equivalence relation, where for any objects a, b, and c:transitive *a*=*a*(reflexive property),- if
*a*=*b*then*b*=*a*(symmetric property), and - if
*a*=*b*and*b*=*c*then*a*=*c*(transitive property).

as a consequence of the reflexive, symmetric, and transitive properties, any equivalence relation provides a

of the underlying set into disjointpartition . two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.equivalence classes - notation
- definition
- examples
- connections to other relations
- well-definedness under an equivalence relation
- equivalence class, quotient set, partition
- fundamental theorem of equivalence relations
- comparing equivalence relations
- generating equivalence relations
- algebraic structure
- equivalence relations and mathematical logic
- euclidean relations
- see also
- notes
- references
- external links

In **equivalence relation** is a

*a*=*a*(reflexive property),- if
*a*=*b*then*b*=*a*(symmetric property), and - if
*a*=*b*and*b*=*c*then*a*=*c*(transitive property).

As a consequence of the reflexive, symmetric, and transitive properties, any equivalence relation provides a