Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Check whether the relation R in R defined by R = {(a, b) : a is less than or equal to b to the power 3 } is reflexive, symmetric or transitive.

Q.5 Check whether the relation R in R defined by R = \{(a, b) : a \leq b^3 \} is reflexive,
symmetric or transitive.

 

Answers (1)

best_answer

R = \{(a, b) : a \leq b^3 \}

\left ( \frac{1}{2},\frac{1}{2} \right )\notin R     because     \frac{1}{2}\nleqslant (\frac{1}{2}) ^{3}

So, it is not symmetric

 

Now, \left ( 1,2 \right ) \in R    because 1< 2^{3}

but \left ( 2,1 \right )\notin R  because 2\nleqslant 1^{3}

It is not symmetric

\left ( 3,1.5 \right ) \in R\, \, and \, \, \left ( 1.5,1.2 \right ) \in R   as   3< 1.5^{3} \, \, and \, \, 1.5< 1.2^{3}.

But, \left ( 3,1.2 \right )\notin R   because 3 \nleqslant 1.2^{3}

So it is not transitive

Thus, it is neither reflexive, nor symmetric,nortransitive.

 

 

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

CBSE Results 2024: Marks verification from 4th day of result declaration; board issues schedule
anam-khan

CBSE 10th, 12th results 2024 ‘shortly’; board issues Digilocker access code for students
anam-khan

CBSE Class 10, 12 results 2024 likely after May 20, says result portal

Latest Question