Let $A=\{-2,-1,0,1,2,3\}$. let R be a relation on A defined by $x R y$ if and only if $y=\max \{x, 1\}$. Let…

Let $A=\{-2,-1,0,1,2,3\}$. let R be a relation on A defined by $x R y$ if and only if $y=\max \{x, 1\}$. Let $l$ 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 $l+\mathrm{m}+\mathrm{n}$ is equal to
  1. $12$
  2. $11$
  3. $13$
  4. $14$

Solution

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

Asked in: JEE Main 2025 (03 Apr Shift 2)

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