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

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

Aicharya · Accepted Answer

$\begin{aligned} & \begin{array}{l}2 \mathrm{x}-\mathrm{y}=0 \ \{0,0\}\{-1,-2\}\{1,2\} \ 2 \mathrm{x}-\mathrm{y}=1\end{array} \ & \{0,-1\}\{1,1\}\{2,3\}\{-1,-3\} \ & 	ext { Total }(0,0)(-1,-2),(1,2)(0,-1),(1,1)(2,3)(-1,-3) \ & 	ext { Reflexive } \quad \mathrm{m}=5 \quad \& \ell=7 \ & 	ext { Symm. } \quad \mathrm{n}=5 \quad \ell+\mathrm{m}+\mathrm{n}=17 \ & 	ext { option (2) }\end{aligned}$ .

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

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