Practice Problems on Transitive Relation
Problem 1: Let R be a relation on the set of all integers defined as follows: For any integers a and b, (a, b) is in R if and only if a is a multiple of b. Determine whether R is a transitive relation.
Problem 2: Consider the set A = {1, 2, 3, 4, 5} and define a relation R on A such that (x, y) is in R if and only if x is greater than y. Determine whether R is a transitive relation.
Problem 3: Let S be a set of all people, and define a relation R on S as follows: (x, y) is in R if and only if x is a sibling of y. Determine whether R is a transitive relation.
Problem 4: Given a set A = {a, b, c, d, e}, define a relation R on A such that (x, y) is in R if and only if the sum of the ASCII values of the characters in x is greater than the sum of the ASCII values of the characters in y. Determine whether R is a transitive relation.
Problem 5: Consider a relation R on the set of real numbers defined as follows: (x, y) is in R if and only if |x – y| ≤ 1. Determine whether R is a transitive relation.
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