Symmetric relation

Definition

Let $R$ be a binary relation on a set $A$. The relation $R$ is symmetric when, for all $a, b \in A$, $a \mathrel{R} b$ implies $b \mathrel{R} a$.

Remarks

Equality is symmetric. The relation $\le$ on $\mathbb{R}$ is not symmetric, because $1 \le 2$ but not $2 \le 1$. A relation $R$ is symmetric exactly when it is equal to its converse.

Explanations

L1 human

"Is a sibling of" is symmetric: if Ann is a sibling of Bob, then Bob is a sibling of Ann. "Is a parent of" is not symmetric.