Sets, Relations and Function: Let R_1 and R_2 be two relations defined on mathbbR by… | JEE Main 2022

JEE Main 2022 (Online) 27th July Morning ShiftQuestion 1

Let $R_1$ and $R_2$ be two relations defined on $\mathbb{R}$ by $aR_1b\Leftrightarrow ab\ge0$ and $aR_2b\Leftrightarrow a\ge b$. Then,

Sets, Relations and Function

$R_1$ is an equivalence relation but not $R_2$$R_2$ is an equivalence relation but not $R_1$both $R_1$ and $R_2$ are equivalence relationsneither $R_1$ nor $R_2$ is an equivalence relation✓ Correct answer

Solution

$R_1$: $ab\ge0$ is reflexive and symmetric but not transitive: $1R_10$, $0R_1(-1)$, yet $1\cdot(-1)<0$. $R_2$: $a\ge b$ is not symmetric ($2\ge1$ but $1\not\ge2$). Neither is an equivalence relation: option D.

Sets, Relations and Function - JEE Mathematics question (JEE Main 2022 (Online) 27th July Morning Shift)

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