Category:Transitive Relations
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This category contains results about transitivity of relations.
Let $\RR \subseteq S \times S$ be a relation in $S$.
$\RR$ is transitive if and only if:
- $\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \in \RR$
that is:
- $\set {\tuple {x, y}, \tuple {y, z} } \subseteq \RR \implies \tuple {x, z} \in \RR$
Subcategories
This category has the following 8 subcategories, out of 8 total.
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Pages in category "Transitive Relations"
The following 43 pages are in this category, out of 43 total.
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- Reflexive and Symmetric Relation is not necessarily Transitive
- Reflexive and Transitive Relation is Idempotent
- Reflexive and Transitive Relation is not necessarily Symmetric
- Reflexive Closure of Transitive Antisymmetric Relation is Ordering
- Reflexive Relation on Set of Cardinality 2 is Transitive
- Relation Induced by Strict Positivity Property is Transitive
- Relation is Reflexive Symmetric and Antisymmetric iff Diagonal Relation
- Relation Isomorphism Preserves Transitivity
- Relation on Set of Cardinality 1 is Symmetric and Transitive
- Relation on Set of Cardinality 2 cannot be Non-Symmetric and Non-Transitive
- Relations with Combinations of Reflexivity, Symmetry and Transitivity Properties
- Restriction of Antitransitive Relation is Antitransitive
- Restriction of Non-Transitive Relation is Not Necessarily Non-Transitive
- Restriction of Transitive Relation is Transitive