JEE Main 2022 · 27 Jul · Shift 1 · Mathematics Q1

MathematicsSingle correct+4 / -1Question 1 of 90

Let $R_1$ and $R_2$ be two relations defined on $\mathbf R$ by

$a\,R_1\,b\Leftrightarrow ab\ge0$ and $a\,R_2\,b\Leftrightarrow a\ge b$

Then,

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 relations

neither

R_1

nor

R_2

is an equivalence relation

Answer and worked solution

Official answer: D

$R_1$ is reflexive and symmetric but not transitive: $1R_10$ and $0R_1(-1)$ , yet $1\cdot(-1)<0$ .

$R_2$ is not symmetric ( $2\ge1$ but not $1\ge2$ ).

Neither is an equivalence relation. (D)

JEE Main 2022 · 27 Jul · Shift 1, Mathematics question 1