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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 :

  1. A Equivalence
  2. B Transitive only
  3. C Reflexive only
  4. D Symmetric only
Verified Solution

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…