For the relation \(R = \{(a, b): a \le b\}\) in \(R\), which of the following is correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → It is reflexive and transitive but not symmetric
Here the relation is defined on the set R of real numbers.
Reflexive: \(a \le a\) for every real a, so \((a, a) \in R\). Reflexive.
Symmetric: \((1, 2) \in R\) since \(1 \le 2\), but \((2, 1) \notin R\) since \(2 \le 1\) is false. Not symmetric.
Transitive: if \(a \le b\) and \(b \le c\), then \(a \le c\). Transitive.
So R is reflexive and transitive but not symmetric.
NCERT (2026-27 edition):
Types of Relations
