Relation R on the set A = {1, 2, 3, …, 13, 14} defined as R = {(x, y) : 3x − y = 0} is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither reflexive nor symmetric nor transitive
3x − y = 0 means y = 3x. With both x and y in A = {1, 2, …, 14}, the relation in roster form is
\(R = \{(1, 3), (2, 6), (3, 9), (4, 12)\}\)
Reflexive: (1, 1) ∉ R, since 3 × 1 ≠ 1. Not reflexive.
Symmetric: (1, 3) ∈ R but (3, 1) ∉ R. Not symmetric.
Transitive: (1, 3) ∈ R and (3, 9) ∈ R, but (1, 9) ∉ R. Not transitive.
NCERT (2026-27 edition):
Types of Relations
