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JEE Main 202523 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
23 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 23 January · Morning Shift · Mathematics · Sets and Relations

Let R=\ (1,2),(2,3),(3,3)\ be a relation defined on the set \...

Let R={(1,2),(2,3),(3,3)}\mathrm{R}=\{(1,2),(2,3),(3,3)\} be a relation defined on the set {1,2,3,4}\{1,2,3,4\}. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

Options

  1. A1010
  2. B77
  3. C88
  4. D99

Correct answer

B. 77

Step-by-step solution

A={1,2,3,4}A=\{1,2,3,4\} For relation to be reflexive R={(1,2),(2,3),(3,3)}\mathrm{R}=\{(1,2),(2,3),(3,3)\} Minimum elements added will be (1,1),(2,2),(4,4)(2,1)(3,2)(3,2)(3,1)(1,3)(1,1),(2,2),(4,4)(2,1)(3,2)(3,2)(3,1)(1,3) ∴\therefore Minimum number of elements =7=7
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