Chapter 1 - Relations And Functions
NCERT Solutions for Class 12 Science Math
Exercise No. 1.1
Question 5:Check whether the relation R in R defined as R = {(a, b): a ≤ b3} is reflexive, symmetric or transitive.
ANSWER:
R = {(a, b): a ≤ b3}
It is observed that![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/230/5993/Chapter%201_html_m17570f67.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/230/5993/Chapter%201_html_m17570f67.gif)
∴ R is not reflexive.
Now,
(1, 2) ∈ R (as 1 < 23 = 8)
But,
(2, 1) ∉ R (as 2 > 13 = 1)
∴ R is not symmetric.
We have![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/230/5993/Chapter%201_html_29fcd0f.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/230/5993/Chapter%201_html_29fcd0f.gif)
But ![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/230/5993/Chapter%201_html_3ca0076b.gif)
![](https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/230/5993/Chapter%201_html_3ca0076b.gif)
∴ R is not transitive.
Hence, R is neither reflexive, nor symmetric, nor transitive.