Consider the relation … on the set ……

Single correct+4 / -1Answer matches NTA’s final key

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

Only I is true
Only II is true
Both I and II are true
Neither I nor II is true

Solution

Count the pairs. $1 + ab > 0$ means $ab \ge 0$ , since $ab$ is an integer.

If $a = 0$ or $b = 0$ : $ab = 0$ , which works. That gives $5 + 5 - 1 = 9$ pairs.
Otherwise $a, b$ must have the same sign: both in $\{1, 2\}$ gives $4$ pairs, both in $\{-1, -2\}$ gives $4$ pairs.

So $|R| = 9 + 4 + 4 = 17$ . Statement I is true.

Equivalence? $R$ is reflexive ( $1 + a^2 > 0$ ) and symmetric ( $ab = ba$ ), but not transitive: $(1, 0) \in R$ and $(0, -1) \in R$ , yet $1 + (1)(-1) = 0$ , so $(1, -1) \notin R$ . Statement II is false.

Answer: only I is true.

Answer checked against the official answer key. The solution is our own working.

JEE MAIN 2026 · Sets, Relations and Functions

Solution

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