Let R₁ and R₂ be two relations defined on R by a R₁ b a b ≥ 0 and a R₂ b a ≥ b Then,

(D) neither R₁ nor R₂ is an equivalence relation

(A) R₁ is an equivalence relation but not R₂

(B) R₂ is an equivalence relation but not R₁

(C) both R₁ and R₂ are equivalence relations

Sets, Relations and Functions: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Morning shift · Q5382

JEE Main 202227 Jul, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

R_{1}

and

R_{2}

be two relations defined on

\mathbb{R}

a \,R_{1} \,b \Leftrightarrow a b \geq 0

and

a \,R_{2} \,b \Leftrightarrow a \geq b

Then,

JEE Main 2022 · 27 Jul, Morning shift · Q5382

JEE Main 202227 Jul, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

R_{1}

and

R_{2}

be two relations defined on

\mathbb{R}

a \,R_{1} \,b \Leftrightarrow a b \geq 0

and

a \,R_{2} \,b \Leftrightarrow a \geq b

Then,