Sets, Relations and Function: Let R be a relation on mathbbZtimesmathbbZ defined by (a,b)R(c,d) if… | JEE Main 2024

JEE Main 2024 (Online) 29th January Morning ShiftQuestion 1

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

Sets, Relations and Function

Reflexive and transitive but not symmetricReflexive and symmetric but not transitive✓ Correct answerReflexive, symmetric and transitiveReflexive but neither symmetric nor transitive

Solution

Reflexive: $ab-ba=0$. Symmetric: $ad-bc$ divisible by 5 $\Rightarrow cb-da$ too. Not transitive: $(1,0)R(0,0)$, $(0,0)R(0,1)$ but $1\cdot1-0=1$ not divisible by 5, so $(1,0)\not R(0,1)$. Option (B).

Sets, Relations and Function - JEE Mathematics question (JEE Main 2024 (Online) 29th January Morning Shift)

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