A relation R on the set \(A = \{1, 2, 3, \ldots, 13, 14\}\) 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 \(y = 3x\). Both x and y must lie in A, so \(y = 3x \le 14\) and \(x \le 4\):
\(R = \{(1, 3), (2, 6), (3, 9), (4, 12)\}\)
Reflexive: no. \((1, 1) \notin R\), since \(3 \times 1 - 1 = 2 \ne 0\).
Symmetric: no. \((1, 3) \in R\), but \((3, 1) \notin R\).
Transitive: no. \((1, 3) \in R\) and \((3, 9) \in R\), but \((1, 9) \notin R\).
NCERT (2026-27 edition):
Types of Relations
