# 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

**Solution:**

R = {(a, b) : a ≤ b^{2}}

(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 1^{2}

(4, 1) ∉ R

Therefore,

R is not symmetric.

(3, 2)(2, 1.5) ∈ R

[Because 3 < 2^{2} = 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

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 ≤ b^{2}} is neither reflexive nor symmetric nor transitive

**Summary:**

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