Symmetric closure
In mathematics, the symmetric closure of a binary relation on a set is the smallest symmetric relation on that contains
For example, if is a set of airports and means "there is a direct flight from airport to airport ", then the symmetric closure of is the relation "there is a direct flight either from to or from to ". Or, if is the set of humans and is the relation 'parent of', then the symmetric closure of is the relation " is a parent or a child of ".
Definition
The symmetric closure of a relation on a set is given by
In other words, the symmetric closure of is the union of with its converse relation,
See also
- Transitive closure – Smallest transitive relation containing a given binary relation
- Reflexive closure – operation on binary relationsPages displaying wikidata descriptions as a fallback
References
- Franz Baader and Tobias Nipkow, Term Rewriting and All That, Cambridge University Press, 1998, p. 8
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