Properties of Asymmetric Relation
- Empty relation on any set is always asymmetric.
- Every asymmetric relation is also irreflexive and anti-symmetric.
- Universal relation over a non-empty set is never asymmetric.
- A non-empty relation can not be both symmetric and asymmetric.
Asymmetric Relation on a Set
A relation is a subset of the cartesian product of a set with another set. A relation contains ordered pairs of elements of the set it is defined on. To learn more about relations refer to the article on “Relation and their types“.
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