ExamBro
ExamBro
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:

  1. A Reflexive only
  2. B Reflexive and symmetric only
  3. C Symmetric and transitive only
  4. D Equivalence
Verified Solution

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 \(k_1, k_2\).…