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:

$\RR^+ = \set {\tuple {1, 2}, \tuple {2, 2}, \tuple {2, 3}, \tuple {1, 3} }$

Sources

• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.5$ Relations: Closures of Relations