Transitive Relation Example
Some examples of transitive relationships are:
- A is Subset of B
- x is Divisibile by y
- A Is Equals to B
- △1 is Conguents to △2
- this Implies that
Let’s see an example in detail.
Example: Consider a set of natural numbers and define a relation R as follows: (1, 2), (2, 3), (1, 3). Check if relation R is transitive.
Solution:
(1, 2) and (2, 3) we must verify if (1, 3) also belongs to R.
In this relation:
- (1, 2) implies that 1 is related to 2.
- (2, 3) implies that 2 is related to 3.
- (1, 3) implies that 1 is related to 3.
Since (1, 3) is indeed part of R, we conclude that relation R is transitive.
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