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

<p>$$\begin{aligned} &\begin{aligned} & x R y \Leftrightarrow 2 x-y \in\{0,1\} \\ & \Rightarrow \quad y=2 x \text { or } y=2 x-1 \\ & A=\{-3,-2,-1,0,1,2,3\} \\ & \mathrm{R}=\{(-1,-2),(0,0),(1,2),(-1,-3),(0,-1),(1,1), \\ & (2,3)\} \\ & \Rightarrow \quad I=7 \end{aligned}\\ &\text { For } R \text { to be reflexive }(0,0),(1,1) \in R \end{aligned}$$</p> <p>But other $(a, a)$ such that $2 a-a \in\{0,1\}$</p> <p>$\Rightarrow \quad a \in\{0,1\}$</p> <p>5 other pairs needs to be added $\Rightarrow m=5$</p> <p>$x R y \Rightarrow y R x$ to be symmetric</p> <p>$(-1,-2) \Rightarrow(-2,-1)$</p> <p>$(1,2) \Rightarrow(2,1)$</p> <p>$(-1,-3) \Rightarrow(-3,-1)$</p> <p>$(0,-1) \Rightarrow(-1,0)$</p> <p>$(2,3) \Rightarrow(3,2) \Rightarrow 5$ needs to be added, $n=5$</p> <p>$\Rightarrow \quad l+m+n=17$</p>