Relation in a set E so that for every ordered pair (x, y) of distinct elements of E, we have either (x, y), or (y, x), but never both at the same time.
In the arrow representation of an asymmetric relation, the relation is connected if there is exactly one arrow between every pair of distinct elements.
Examples
- The relation “…is less than…” in the set E = {2, 3, 4, 5, 6} is an asymmetric relation.
- In a set of numbers, the relations of inequalities in the strict sense, like < and >, are asymmetric relations.