Check whether the relation R in R defined by R = {(a, b) : a ≤ b³} is reflexive, symmetric or transitive

Solution:

R = {(a, b) : a ≤ b³}

(1/2, 1/2) ∈ R, since 1/2 > (1/2)³

Therefore,

R is not reflexive.

(1, 2) ∈ R (as 1 < 2³ = 8)

(2,1) ∉ R (as 2³ > 1 = 8)

Therefore,

R is not symmetric.

(3, 3/2), (3/2, 6/5) ∈ R, since 3 < (3/2)³ and 2/3 < (6/2)³

(3, 6/5) ∉ R 3 > (6/5)³

Therefore,

R is not transitive.

R is neither reflexive nor symmetric nor transitive

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 5

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

Summary:

The relation R in R defined by R = {(a, b) : a ≤ b³} is neither reflexive nor symmetric nor transitive. An equivalence relation shows reflexive, transitive, and symmetric property