Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is (A) 1 (B) 2 (C) 3 (D) 4

Q. 17 Let A = \{1, 2, 3\}. Then number of equivalence relations containing (1, 2) is
(A) 1
(B) 2
(C) 3
(D) 4

Answers (1)

best_answer

A = \{1, 2, 3\}

The number of equivalence relations containing  (1, 2) is given by 

R = \left \{ (1,1),(2,2),(3,3),(1,2),(2,1) \right \}

We are left with four  pairs (2,3) ,(3,2),(1,3),(3,1) .

(1,1),(2,2),(3,3) \in R  , so relation R is reflexive.

(1,2),(2,1) \in R    and   (2,3),(3,2) \notin R  , so relation R is not symmetric.

 (1,3),(3,1) \notin R  , so realation R is not transitive.

Hence , equivalence relation is bigger than R  is universal relation.

Thus the total number of equivalence relations containing   (1,2) is two.

Thus, option B is correct.

Posted by

seema garhwal

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

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
anam-khan

Board Exams: States agree to equivalence; no question paper ‘jumbling’ from next year, says PARAKH CEO

Latest Question