JEE Main 2026 — Sets and Relations Question with Solution

The set is $A=\{-2,-1,0,1,2\}$.

For Statement I, the relation is defined as $(a,b)\in R⟺1+ab>0$.
The pairs $(a,b)$ that do not belong to $R$ satisfy $1+ab\le 0\Rightarrow ab\le -1$.
The pairs satisfying $ab\le -1$ are $(-2,1),(-2,2),(-1,1),(-1,2),(1,-2),(1,-1),(2,-2),(2,-1)$.
There are $8$ such pairs.
The total number of pairs in $A\times A$ is $5\times 5=25$.
The number of elements in $R$ is $25-8=17$.
Thus, Statement I is true.

For Statement II, checking transitivity gives $(-2,0)\in R$ since $1+(-2)(0)=1>0$.
Also, $(0,2)\in R$ since $1+(0)(2)=1>0$.
However, $(-2,2)\notin R$ since $1+(-2)(2)=-3\le 0$.
Since $R$ is not transitive, it is not an equivalence relation.
Thus, Statement II is false.

Answer: Only I is true