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Return to Symmetric

Snippet from Wikipedia: Symmetric relation

A symmetric relation is a type of binary relation. A homogeneous relation ${\displaystyle R}$ on a set ${\displaystyle X}$ is symmetric if:

for all ${\displaystyle a}$ and ${\displaystyle b}$ in ${\displaystyle X}$, ${\displaystyle aRb}$ if and only if ${\displaystyle bRa}$,

where the notation ${\displaystyle aRb}$ means that the ordered pair ${\displaystyle (a,b)}$ is in the relation ${\displaystyle R}$.

An example is the relation "is equal to", because if a = b is true then b = a is also true. If R^T represents the converse of R, then R is symmetric if and only if R = R^T.

Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation.

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