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