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

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.

R = {(a, b): a ≤ 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.