CUET · MATHS · PYQ PAPER 2025
If \(R\) be a relation on the set of integers \(Z\), given by \(R=\{(a, b):(a-b)\) is a multiple of 3\(\}\), then \(R\) is :
- A Reflexive, Symmetric but not Transitive
- B Reflexive, Transitive but not Symmetric
- C Symmetric, Transitive, but not Reflexive
- D an equivalence relation
Answer & Solution
Correct Answer
(D) an equivalence relation
Step-by-step Solution
Detailed explanation
Reflexive: For any \(a \in Z\), \(a-a = 0\), which is a multiple of 3. So, \((a,a) \in R\). Symmetric: If \((a,b) \in R\), then \(a-b = 3k\) for some integer \(k\). Then \(b-a = -(a-b) = -3k = 3(-k)\). So, \((b,a) \in R\). Transitive: If \((a,b) \in R\) and \((b,c) \in R\), then…
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