Category:Antisymmetric Relations
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This category contains results about Antisymmetric Relations.
Definitions specific to this category can be found in Definitions/Antisymmetric Relations.
$\RR$ is antisymmetric if and only if:
- $\tuple {x, y} \in \RR \land \tuple {y, x} \in \RR \implies x = y$
that is:
- $\set {\tuple {x, y}, \tuple {y, x} } \subseteq \RR \implies x = y$
Subcategories
This category has only the following subcategory.
E
Pages in category "Antisymmetric Relations"
The following 16 pages are in this category, out of 16 total.
E
I
R
- Reflexive Closure of Transitive Antisymmetric Relation is Ordering
- Relation is Antisymmetric and Reflexive iff Intersection with Inverse equals Diagonal Relation
- Relation is Antisymmetric iff Intersection with Inverse is Coreflexive
- Relation is Reflexive Symmetric and Antisymmetric iff Diagonal Relation
- Relation is Symmetric and Antisymmetric iff Coreflexive
- Relation Isomorphism Preserves Antisymmetry
- Restriction of Antisymmetric Relation is Antisymmetric