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JEE Main 22-Jan-2025 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 22-Jan-2025 Paper - Shift 14 Marks
MCQ
The number of non-empty equivalence relations on the set {1,2,3} is:
  • A
    6
  • B
    7
  • ✓
    5
  • D
    4
✓

Answer

Correct option: C.
5
(C) 5
Sol. Let R be the required relation
$
A=\{(1,1)(2,2),(3,3)\}
$
(i) $| R |=3$, when $R = A$
(ii) $| R |=5$, e.g. $R = A \cup\{(1,2),(2,1)\}$
Number of $R$ can be [3]
(iii) $R =\{1,2,3\} \times\{1,2,3\}$
Ans. (5)

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