JEE Main 2025 (Online) 4th April Evening ShiftQuestion 1
Let $A=\{-3,-2,-1,0,1,2,3\}$ and $R$ be a relation on $A$ defined by $xRy$ if and only if $2x-y\in\{0,1\}$. 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 $l+m+n$ is equal to :
Sets, Relations and Function
Solution
$R=\{(x,y):y=2x\text{ or }y=2x-1\}$ on $A=\{-3..3\}$: $y=2x$: $x=-1,0,1$ (3 pairs); $y=2x-1$: $x=-1,0,1,2$ gives $-3,-1,1,3$ (4 pairs). So $l=7$. Reflexive: $(x,x)\in R$ iff $x\in\{0,1\}$, so $m=7-2=5$. Symmetric: reverse pairs present: $(0,0),(1,1)$ only. Others $5$ need their reverses (distinct and not present), so $n=5$. $l+m+n=17$. Option C.