# Definition:Symmetry (Relation)/Antisymmetric and Asymmetric

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## Antisymmetric and Asymmetric Relations

Note the difference between:

- An asymmetric relation, in which the fact that $\tuple {x, y} \in \RR$ means that $\tuple {y, x}$ is definitely
*not*in $\RR$

and:

- An antisymmetric relation, in which there
*may*be instances of both $\tuple {x, y} \in \RR$ and $\tuple {y, x} \in \RR$ but if there are, then it means that $x$ and $y$ have to be the same object.