Let L be the set of all lines in a plane and R be the relation in L defined as \(R = \{(l_1, l_2) : l_1 \text{ is perpendicular to } l_2, \text{ where } l_1, l_2 \in L\}\). Choose the correct answer:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → R is symmetry relation
Reflexive: no line is perpendicular to itself, so \((l_1, l_1) \notin R\). R is not reflexive.
Symmetric: if \(l_1\) is perpendicular to \(l_2\), then \(l_2\) is perpendicular to \(l_1\). So \((l_1, l_2) \in R \Rightarrow (l_2, l_1) \in R\), and R is symmetric.
Transitive: if \(l_1 \perp l_2\) and \(l_2 \perp l_3\), then in a plane \(l_1\) is parallel to \(l_3\), not perpendicular to it. So R is not transitive.
Since R is not reflexive or transitive, it is not an equivalence relation. R is symmetric only.
NCERT (2026-27 edition):
Types of Relations
