transitive relation

A relation^{👁 Mathworld
👁 Planetmath}
on a set is transitive^{👁 Mathworld
👁 Planetmath
👁 Planetmath
👁 Planetmath
👁 Planetmath}
if and only if , .

For example, the “is a subset of” relation on any set of sets is transitive. The “less than” relation on the set of real numbers is also transitive.

The “is not equal to” relation on the set of integers is not transitive, because and does not imply .