Let L be the set of all lines in a plane and R be the relation on set L defined by \(R = \{(L_1, L_2): L_1 \perp L_2\}\). Then R is
(A) an equivalence Relation
(B) a symmetric Relation
(C) not a transitive Relation
(D) a reflexive Relation
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (C) only
R relates two lines of the plane exactly when they are perpendicular. Each property is checked against this.
(A) an equivalence Relation — Incorrect. No line is perpendicular to itself, so R is not reflexive.
(B) a symmetric Relation — Correct. If \(L_1 \perp L_2\), then \(L_2 \perp L_1\), so \((L_1, L_2) \in R\) gives \((L_2, L_1) \in R\).
(C) not a transitive Relation — Correct. In a plane, if \(L_1 \perp L_2\) and \(L_2 \perp L_3\), then \(L_1\) is parallel to \(L_3\), not perpendicular to it:
\((L_1, L_2) \in R\) and \((L_2, L_3) \in R\), but \((L_1, L_3) \notin R\)
(D) a reflexive Relation — Incorrect. No line is perpendicular to itself, so \((L, L) \notin R\).
NCERT (2026-27 edition):
Types of Relations
