CUET · MATHS · PYQ PAPER 2023
The relation \(R\) on the set \(A=\{1,2,3,4,5\}\), given by \(R(a, b):|a-b|\) is even, is:
- A Reflexive only
- B Reflexive and symmetric only
- C Symmetric and transitive only
- D Equivalence
Answer & Solution
Correct Answer
(D) Equivalence
Step-by-step Solution
Detailed explanation
\(|a-a| = 0\), which is even. R is reflexive. If \((a,b) \in R\), \(|a-b|\) is even. Since \(|b-a| = |a-b|\), then \(|b-a|\) is even. R is symmetric. If \((a,b) \in R\) and \((b,c) \in R\): \(a-b=2k_1\), \(b-c=2k_2\) for some integers \(k_1, k_2\).…
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