JEE Main 2025 (Online) 3rd April Evening ShiftQuestion 1
Let $A=\{-2,-1,0,1,2,3\}$. Let $R$ be a relation on $A$ defined by $xRy$ 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 $l+m+n$ is equal to
Sets, Relations and Function
Solution
$R=\{(-2,1),(-1,1),(0,1),(1,1),(2,2),(3,3)\}$, so $l=6$. Reflexive: missing $(-2,-2),(-1,-1),(0,0)$, so $m=3$. Symmetric: reverses needed $(1,-2),(1,-1),(1,0)$ ($(1,1),(2,2),(3,3)$ are self-symmetric): $n=3$. $l+m+n=12$. Option B.