Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b²} is neither reflexive nor symmetric nor transitive

Solution:

R = {(a, b) : a ≤ b²}

(1/2, 1/2) ∈ R because 1/2 > (1/2)

Therefore,

R is not reflexive.

(1, 4) ∈ R as 1 < 4 .

But 4 is not less than 1²

(4, 1) ∉ R

Therefore,

R is not symmetric.

(3, 2)(2, 1.5) ∈ R

[Because 3 < 2² = 4 and 2 < (1.5)² = 2.25]

3 > (1.5)² = 2.25

⇒ (3,1.5) ∉ R

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 2

Show that the relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive

Summary:

The relation R in the set R of real numbers, defined as R = {(a, b): a ≤ b²} is neither reflexive nor symmetric nor transitive