===== Equivalence relation =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X$ |

| @#FFBB00: definiendum | @#FFBB00: $ \sim \in \text{EquivRel}(X) $ |

| @#55CCEE: context     | @#55CCEE: $ \sim  \in \mathrm{Rel}(X) $ |
| $x,y,z\in X$ |

| @#55EE55: postulate   | @#55EE55: $ x\sim x $ |
| @#55EE55: postulate   | @#55EE55: $ x\sim y \Leftrightarrow y\sim x $ |
| @#55EE55: postulate   | @#55EE55: $ x\sim y \land y\sim z \Leftrightarrow x\sim z $ |

==== Discussion ====
The relation $\sim$ is an equivalence relation, if it's in the intersection of all reflexive, all symmetric and all transitive relation. Hence 
=== Reference ===
Wikipedia: [[http://en.wikipedia.org/wiki/Equivalence_relation|Equivalence relation]]
==== Parents ====
=== Subset of ===
[[Reflexive relation]], [[Symmetric relation]], [[Transitive relation]]