JEE Main 2024 (Online) 6th April Evening ShiftQuestion 1
Let $A=\{1,2,3,4,5\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x\le5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A\times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m+n$ is equal to :
Sets, Relations and Function
Solution
$4x\le5y$: counting over $A\times A$ gives $m=16$ (pairs with $y\ge 4x/5$). Reverse pairs missing from $R$: $n=9$. $m+n=25$. Option (C).