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JEE Main 202522 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
22 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 22 January · Morning Shift · Mathematics · Sets and Relations

The number of non-empty equivalence relations on the set \ 1,2,3\...

The number of non-empty equivalence relations on the set {1,2,3}\{1,2,3\} is :

Options

  1. A66
  2. B55
  3. C77
  4. D44

Correct answer

B. 55

Step-by-step solution

Let RR be the required relation A={(1,1)(2,2),(3,3)}\mathrm{A}=\{(1,1)(2,2),(3,3)\} (i) ∣R∣=3|\mathrm{R}|=3, when R=A\mathrm{R}=\mathrm{A} (ii) ∣R∣=5|\mathrm{R}|=5, e.g. R=A∪{(1,2),(2,1)}\mathrm{R}=\mathrm{A} \cup\{(1,2),(2,1)\} Number of RR can be [3] (iii) R={1,2,3}×{1,2,3}\mathrm{R}=\{1,2,3\} \times\{1,2,3\} Ans. (5)
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