CUET · MATHS · PYQ PAPER 2025
A relation \(R\) on the set \(A=\{1, 2, 3, \ldots, 13, 14\}\) defined as \(R=\{(x, y) : 3 x-y=0\}\) is
- A Reflexive and symmetric but not transitive
- B Neither reflexive nor transitive but symmetric
- C Neither symmetric nor transitive but reflexive
- D Neither reflexive nor symmetric nor transitive
Answer & Solution
Correct Answer
(D) Neither reflexive nor symmetric nor transitive
Step-by-step Solution
Detailed explanation
Reflexive: For \( (a, a) \in R \), \( 3a - a = 0 \Rightarrow 2a = 0 \Rightarrow a = 0 \). But \( a \in A = \{1, \ldots, 14\} \). Thus, not reflexive. Symmetric: Let \( (x, y) \in R \). Then \( y = 3x \). For \( (y, x) \in R \), \( x = 3y \). Substituting \( y=3x \),…
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