Transitive Closure (Relation Theory)/Examples/Arbitrary Example 1

Example of Transitive Closure
Let $S = \set {1, 2, 3}$ be a set.

Let $\RR$ be the relation on $S$ defined as:
 * $\RR = \set {\tuple {1, 2}, \tuple {2, 2}, \tuple {2, 3} }$

The transitive closure $\RR^+$ of $\RR$ is given by:
 * $\RR^+ = \set {\tuple {1, 2}, \tuple {2, 2}, \tuple {2, 3}, \tuple {1, 3} }$