Editing Transitive closure (section)

== Properties ==
The [[Intersection (set theory)|intersection]] of two transitive relations is transitive.

The [[union (set theory)|union]] of two transitive relations need not be transitive. To preserve transitivity, one must take the transitive closure. This occurs, for example, when taking the union of two [[equivalence relation]]s or two [[preorder]]s. To obtain a new equivalence relation or preorder one must take the transitive closure (reflexivity and symmetry—in the case of equivalence relations—are automatic).