The relation R on the set of real numbers defined by R= (a,b): a≤ b^2…

The correct answer is Option (1) → neither reflexive nor symmetric nor transitive

One counterexample is enough to rule out each property.

Reflexive needs \(a \le a^2\) for every real a. Take \(a = \frac{1}{2}\):

    \( \displaystyle \frac{1}{2} \le \frac{1}{4} \) is false.

So \(\left(\frac{1}{2}, \frac{1}{2}\right) \notin R\): R is not reflexive.

Symmetric fails for the pair (1, 2):

    \((1, 2) \in R\) since \(1 \le 2^2 = 4\)
    \((2, 1) \notin R\) since \(2 \le 1^2 = 1\) is false

Transitive fails for 4, −2, 1:

    \((4, -2) \in R\) since \(4 \le (-2)^2 = 4\)
    \((-2, 1) \in R\) since \(-2 \le 1^2 = 1\)
    \((4, 1) \notin R\) since \(4 \le 1^2 = 1\) is false

So R is neither reflexive nor symmetric nor transitive.

NCERT (2026-27 edition):
Types of Relations