Open App

JEE Exam > JEE Videos > Mathematics (Maths) Class 12 > Types of Relations: Reflexive Symmetric Transitive & Equivalence

Types of Relations: Reflexive Symmetric Transitive & Equivalence Video Lecture | Mathematics (Maths) Class 12 - JEE

Q: 5. Give an example of an equivalence relation.

Ans. An example of an equivalence relation is the relation 'is congruent to' in geometry. If two geometric figures have the same shape and size, they are considered congruent. This relation is reflexive because any figure is congruent to itself, symmetric because if figure 'A' is congruent to figure 'B', then 'B' is also congruent to 'A', and transitive because if figure 'A' is congruent to 'B' and 'B' is congruent to 'C', then 'A' is also congruent to 'C'.

	Mathematics (Maths) Class 12 204 videos\|288 docs\|139 tests

Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

Join Course for Free

Top Courses for JEE

View all

FAQs on Types of Relations: Reflexive Symmetric Transitive & Equivalence Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is a reflexive relation?

Ans. A reflexive relation is a relation where every element is related to itself. In other words, for every element 'a' in the set, the relation contains the pair (a, a). For example, the relation "is equal to" is reflexive because every element is equal to itself.

2. Can a relation be both reflexive and symmetric?

Ans. Yes, a relation can be both reflexive and symmetric. Reflexivity means that every element is related to itself, while symmetry means that if 'a' is related to 'b', then 'b' is also related to 'a'. So, a relation can satisfy both properties by containing all the pairs (a, a) for reflexivity and (a, b) for symmetry.

3. What does it mean for a relation to be transitive?

Ans. Transitivity is a property of relations where if 'a' is related to 'b' and 'b' is related to 'c', then 'a' is also related to 'c'. In other words, if there is a chain of relationships, the transitive relation implies that the end elements are also related. For example, if 'x' is a parent of 'y' and 'y' is a parent of 'z', then the transitive relation implies that 'x' is also a parent of 'z'.

4. How can we determine if a relation is an equivalence relation?

Ans. To determine if a relation is an equivalence relation, we need to check three properties: reflexivity, symmetry, and transitivity. If the relation satisfies all three properties, it is an equivalence relation. Reflexivity ensures that each element is related to itself, symmetry guarantees that if 'a' is related to 'b', then 'b' is also related to 'a', and transitivity ensures that the relation follows a chain of relationships.

5. Give an example of an equivalence relation.

Ans. An example of an equivalence relation is the relation "is congruent to" in geometry. If two geometric figures have the same shape and size, they are considered congruent. This relation is reflexive because any figure is congruent to itself, symmetric because if figure 'A' is congruent to figure 'B', then 'B' is also congruent to 'A', and transitive because if figure 'A' is congruent to 'B' and 'B' is congruent to 'C', then 'A' is also congruent to 'C'.

Related Exams

JEE Commerce Humanities/Arts GRE Grade 12 PAT

About this Video

	7.3K Views
	4.82/5 Rating
	Oct 23, 2024 Last updated

Video Description: Types of Relations: Reflexive Symmetric Transitive & Equivalence for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The notes and questions for Types of Relations: Reflexive Symmetric Transitive & Equivalence have been prepared according to the JEE exam syllabus. Information about Types of Relations: Reflexive Symmetric Transitive & Equivalence covers all important topics for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Types of Relations: Reflexive Symmetric Transitive & Equivalence.

Introduction of Types of Relations: Reflexive Symmetric Transitive & Equivalence in English is available as part of our Mathematics (Maths) Class 12 for JEE & Types of Relations: Reflexive Symmetric Transitive & Equivalence in Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free.

Description

Video Lecture & Questions for Types of Relations: Reflexive Symmetric Transitive & Equivalence Video Lecture | Mathematics (Maths) Class 12 - JEE - JEE full syllabus preparation | Free video for JEE exam to prepare for Mathematics (Maths) Class 12.

Information about Types of Relations: Reflexive Symmetric Transitive & Equivalence

Here you can find the meaning of Types of Relations: Reflexive Symmetric Transitive & Equivalence defined & explained in the simplest way possible. Besides explaining types of Types of Relations: Reflexive Symmetric Transitive & Equivalence theory, EduRev gives you an ample number of questions to practice Types of Relations: Reflexive Symmetric Transitive & Equivalence tests, examples and also practice JEE tests.

	Mathematics (Maths) Class 12 204 videos\|288 docs\|139 tests

Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

Join Course for Free

Explore Courses for JEE exam

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

ppt

Objective type Questions

MCQs

Free