Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b^2} is neither reflexive nor symmetric nor transitive

Class 12, NCERT Chapter 1,  Exercise 1.1, Q2

Solution
We have R = {(a,b):}

It can be observed that

(14,14)∉R

Bcoz, 

14>(14)2

 

R is not Reflexive.

Now (1,4)∈R as   1<16

But (4,1)∉R as 

4≮12

Therefore R is not symmetric.

Now (3,2),(2,1.5)∈R                                                     [As 3 < 4  and 2 < 2.25 ]

But 3 > 2.25

Therefore ( 3, 1.5 )∉R

Therefore R is not Transitive.

Hence R is neither reflexive nor symmetric nor transitive.