Question 5: Check whether the relation R in R defined as R = {(a, b): a ≤ b3} is reflexive, symmetric or transitive. Chapter 1 - Relations And Functions

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 = {(ab): a ≤ b3} is reflexive, symmetric or transitive.

ANSWER:

R = {(ab): ≤ b3}
It is observed that
∴ 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
But 
∴ R is not transitive.
Hence, R is neither reflexive, nor symmetric, nor transitive.

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