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JEE Main 20253 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
3 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Sets and Relations

JEE Main 2025 · 3 April · Evening Shift · Mathematics · Sets and Relations

Let A=\ -2,-1,0,1,2,3\ . let R be a relation on A defined by x R y...

Let A={−2,−1,0,1,2,3}A=\{-2,-1,0,1,2,3\}. let R be a relation on A defined by xRyx R y if and only if y=max⁡{x,1}y=\max \{x, 1\}. Let ll be the number of elements in R. Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then l+m+nl+\mathrm{m}+\mathrm{n} is equal to

Options

  1. A1212
  2. B1111
  3. C1313
  4. D1414

Correct answer

A. 1212

Step-by-step solution

A={−2,−1,0,1,2,3}R={(−2,1),(−1,1),(0,1),(1,1),(2,2),(3,3)}ℓ=6 m=3n=3ℓ+m+n=12\begin{aligned} & \mathrm{A}=\{-2,-1,0,1,2,3\} \\ & \mathrm{R}=\{(-2,1),(-1,1),(0,1),(1,1),(2,2),(3,3)\} \\ & \ell=6 \\ & \mathrm{~m}=3 \\ & \mathrm{n}=3 \\ & \ell+\mathrm{m}+\mathrm{n}=12\end{aligned}
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