QJEEM24Ma375c: JEE Main 2024 Mathematics - Class 11 JEEM24Ma375c Solution: Let R be a relation on Z × Z defined by ( a , b ) R ( c , d )…

Question

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Let $R$ be a relation on $Z \times Z$ defined by $(a, b) R (c, d)$ if and only if $a d - b c$ is divisible by 5. Then $R$ is

Accepted Answer

$(a, b) R (a, b)$ as $a b - a b = 0$

Therefore reflexive

Let $(a, b) R (c, d) \Rightarrow a d - b c$ is divisible by 5

$\Rightarrow bc - ad$ is divisible by $5 \Rightarrow (c, d) R (a, b)$

Therefore symmetric

Relation not transitive as $(3, 1) R (10, 5)$ and $(10, 5) R (1, 1)$ but $(3, 1)$ is not related to $(1, 1)$

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