X 上的关系 R 是非对称的，若对所有的 a 和 b 属于 X，若 a 关系到 b，则 b 不关系到 a。

数学上表示为：

.

非对称关系即反对称的非自反关系。

反对称关系

In mathematics, an asymmetric relation is a binary relation on a set X where:

In mathematical notation, this is:

An example is the "less than" relation < between real numbers: if x < y, then necessarily y is not less than x.The "less than or equal" relation ≤, on the other hand, is not asymmetric, because reversing x ≤ x produces x ≤ x and both are true. In general, any relation in which x R x holds for some x (that is, which is not irreflexive) is also not asymmetric.