For the relation $R = \{(a, b): a ≤ b\}$ 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
Given relation: $R = \{(a,b) : a \le b\}$ on $\mathbb{R}$
Reflexive: For every $a \in \mathbb{R}$, $a \le a$ is true. ✔
Symmetric: If $a \le b$, then $b \le a$ need not hold (e.g., $1 \le 2$ but $2 \leq 1$). ✖
Transitive: If $a \le b$ and $b \le c$, then $a \le c$ is true. ✔
Correct option: It is reflexive and transitive but not symmetric.