Properties of Transitive Relations
There are some properties of Transitive Relations that are discussed as follows:
Inverse of a Transitive Relation
The inverse of a transitive relation is itself a Transitive Relations
- For example, if is older than is a relationship that works in a certain way, then is younger than (its opposite) also works the same way.
Union of Two Transitive Relations
- The union of two transitive relations may or may not be a transitive relation.
- Think of it like having two sets of friends. Sometimes, when you bring those two sets together, the way they interact doesn’t follow the same patterns as when they’re separate.
Intersection of Two Transitive Relations
The intersection of two transitive relations is itself a transitive relation.
- For example, if one group of people likes both chocolate and vanilla ice cream, the fact that they like both flavors still fits the same pattern as when they just liked chocolate or vanilla individually.
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Transitive Relations
Transitive Relation is one of the necessary conditions for equivalence relation, as for any relation to be that needs to to Transitive at first. In Transitive Relation, if element A is related to element B and element B is related to element C, then there must also be a relationship between element A and element C, following the same rule or relation. In other words, if A relates to B and B relates to C, then A must relate to C.
This article provides a well-rounded description of the concept of “Transitive Relation”, including definitions, examples, and properties.
Table of Content
- What is a Relation?
- What is Transitive Relation?
- Properties of Transitive Relations
- Other Relations Related to Transitive Relation
- Transitive Property of Congruent Triangles
- Example of Transitive Relation
- Practice Problems on Transitive Relation
- Transitive Relation – FAQs