JEE Main 2026 (Online) 8th April Evening ShiftQuestion 1
Consider the relation $R$ on the set $\{-2,-1,0,1,2\}$ defined by $(a,b)\in R$ if and only if $1+ab>0$. Then, among the statements :
I. The number of elements in $R$ is $17$
II. $R$ is an equivalence relation
Sets, Relations and Function
Solution
$ab>-1\Rightarrow ab\ge0$. Pairs with $ab<0$: $2\cdot2+2\cdot2=8$, so $|R|=25-8=17$ (I true). Transitivity fails: $(1,0),(0,-1)\in R$ but $(1,-1)\notin R$, so II false. Option (A).