Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 11 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Relation Exercise 1.2 Question 11 Maths Textbook Solution.

Answers (1)

Answer: R is an equivalence relation on A
Hint: To prove equivalence relation it is necessary that the given relation should be reflexive, symmetric and transitive.
Given: O\; be\; the\; origin\; and\; R=\left \{ \left (P, Q \right ):OP=OQ \right \} be\; a\; relation \; on\; A \; where\; O\; is \; the\; origin.
Explanation:
Let A be a set of points on a plane.
Reflexivity:
Let\: P \: \epsilon \: A
Since, OP=OP=(P, P) \: \epsilon \: R
R is reflexive.
Symmetric:
Let (P, Q) \: \epsilon \: R \: f\! or\: P, Q \: \epsilon \: A
Then \: OP=OQ
  OQ=OP
(Q, P) \: \epsilon \: R
R is symmetric
Transitive:
Let (P, Q) \: \epsilon \: R\: and\: (Q, S) \: \epsilon \: R
OP=OQ \: \: ...(i)\: and \: \: OQ=OS \: \:....(ii)
Putting  (ii) in (i), we get
OP=OS
(P, S)\: \epsilon \: R
R is transitive
Therefore, R is reflexive, symmetric and transitive.
Thus, R is an equivalence relation on A.

Posted by

infoexpert27

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE wants international boards reined in; letter to education ministry seeks directions for AIU
anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14
anam-khan

CBSE Board Exams 2025: Online portal for availing exemptions by CWSN students opens

Latest Question