Reflexive Transitive Closure/Examples
Jump to navigation
Jump to search
Examples of Reflexive Transitive Closures
Arbitrary Example $1$
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 reflexive transitive closure $\RR^*$ of $\RR$ is given by:
- $\RR^* = \set {\tuple {1, 1}, \tuple {1, 2}, \tuple {2, 2}, \tuple {2, 3}, \tuple {1, 3}, \tuple {3, 3} }$
Arbitrary Example $2$
Let $S = \set {1, 2, 3, 4, 5}$ be a set.
Let $\RR$ be the relation on $S$ defined as:
- $\RR = \set {\tuple {1, 2}, \tuple {2, 3}, \tuple {3, 4}, \tuple {5, 4} }$
The reflexive transitive closure $\RR^*$ of $\RR$ is given by:
- $\RR^* = \set {\tuple {1, 2}, \tuple {1, 3}, \tuple {1, 4}, \tuple {2, 3}, \tuple {2, 4}, \tuple {3, 4}, \tuple {5, 4}, \tuple {1, 1}, \tuple {2, 2}, \tuple {3, 3}, \tuple {4, 4}, \tuple {5, 5} }$