Symmetric Closure/Examples
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Examples of Symmetric Closures
Arbitrary Example $1$
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 symmetric closure $\RR^\leftrightarrow$ of $\RR$ is given by:
- $\RR^* = \set {\tuple {1, 2}, \tuple {2, 3}, \tuple {3, 4}, \tuple {5, 4}, \tuple {2, 1}, \tuple {3, 2}, \tuple {4, 3}, \tuple {4, 5} }$