Asymmetric relation
A binary relation which never occurs in both directions / From Wikipedia, the free encyclopedia
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Not to be confused with Antisymmetric relation.
In mathematics, an asymmetric relation is a binary relation on a set where for all if is related to then is not related to [1]
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Y indicates that the column's property is always true the row's term (at the very left), while ✗ indicates that the property is not guaranteed in general (it might, or might not, hold). For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by Y in the "Symmetric" column and ✗ in the "Antisymmetric" column, respectively. All definitions tacitly require the homogeneous relation be transitive: for all if and then |