What is Transitive Relation?
Transitive Relations or Transitive Relationships are all about maintaining a clear chain of connections among their elements. If element A is connected with element B and element B is connected with element C then it logically follows that element A must also be connected with element C.
Transitive Relation Definition
Mathematically, a relation R on a set A is said to be transitive if, for all elements a, b, and c in set A:
If (a, b) ∈ R and (b, c) ∈ R, then (a, c) ∈ R.
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