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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.

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Location: Sonkhi, Punjab 152112, India

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