Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Check whether the relation R defined on the set  as <img alt="R=\left \{ (

Check whether the relation R defined on the set A=\left \{ 1,2,3,4,5,6 \right \} as R=\left \{ (a,b):b=a+1 \right \} is reflexive, symmetric or transitive.

 

 

 

 
 
 
 
 

Answers (1)

A=\left \{ 1,2,3,4,5,6 \right \}\: \: \: \: \: \: \: R=\left \{ (a,b):b=a+1 \right \}

\therefore R=\left \{ (a,a+1):a,a+1\equiv \left ( 1,2,3,4,5,6 \right ) \right \}

\Rightarrow R=\left \{ (1,2),(2,3),(3,4),(4,5),(5,6) \right \}

(i) Reflexive : 

\left \{ a,a \right \}\not\equiv R\: \forall \: a

eg: \left \{ 1,1 \right \}\equiv R\: \: \: \left \{ 1,1+1 \right \}\Rightarrow \left \{ 1,2 \right \}\equiv R 

but \left \{ 1,1 \right \}\not\equiv R  Not Reflexive

(ii) Symmetric:

\left \{ a,b \right \}\equiv R\: \: \: \: and\: \: \: \left ( b,a \right )\equiv R

eg: (1,2)\equiv R\: \: but (2,1) \not\equiv R

Not Symmetric

(iii)Transitive:

(a,b)\equiv R\: \: but (b,c) \not\equiv R\: \: \: Thus

(1,2)\equiv R\: \: \: \: \left \{ 2,3 \right \}\equiv R\: \: \: \: but (1,3) \not\equiv R\: \: \: \left \{ 1,1+2 \right \}=\left \{ 1,3 \right \}\not\equiv R

Not Transitive

Posted by

Ravindra Pindel

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 practical exams 2026 will be cancelled over non-compliance with guidelines, says board

Latest Question