Let \(R=\{(L_1,L_2): L_1 \perp L_2 \text{ where } L_1, L_2 \in L \text{ (set of straight line in a plane)}\}\), then
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → R is symmetric but neither reflexive nor transitive
Reflexive: no line is perpendicular to itself, so \((L_1, L_1) \notin R\). R is not reflexive.
Symmetric: if \(L_1 \perp L_2\), then \(L_2 \perp L_1\). So \((L_1, L_2) \in R\) gives \((L_2, L_1) \in R\), and R is symmetric.
Transitive: let \(L_1 \perp L_2\) and \(L_2 \perp L_3\). In a plane, two lines perpendicular to the same line are parallel, so \(L_1 \parallel L_3\) and \(L_1\) is not perpendicular to \(L_3\). So \((L_1, L_3) \notin R\), and R is not transitive.
NCERT (2026-27 edition):
Types of Relations
