jee-main 2022 Q70

jee-main · India · session2_27jul_shift1 Not Maths
Let $R _ { 1 }$ and $R _ { 2 }$ be two relations defined on $\mathbb { R }$ by $a \mathrm { R } _ { 1 } b \Leftrightarrow a b \geq 0$ and $a R _ { 2 } b \Leftrightarrow a \geq b$, then
(1) $R _ { 1 }$ is an equivalence relation but not $R _ { 2 }$
(2) $R _ { 2 }$ is an equivalence relation but not $R _ { 1 }$
(3) both $R _ { 1 }$ and $R _ { 2 }$ are equivalence relations
(4) neither $R _ { 1 }$ nor $R _ { 2 }$ is an equivalence relation
Let $R _ { 1 }$ and $R _ { 2 }$ be two relations defined on $\mathbb { R }$ by $a \mathrm { R } _ { 1 } b \Leftrightarrow a b \geq 0$ and $a R _ { 2 } b \Leftrightarrow a \geq b$, then\\
(1) $R _ { 1 }$ is an equivalence relation but not $R _ { 2 }$\\
(2) $R _ { 2 }$ is an equivalence relation but not $R _ { 1 }$\\
(3) both $R _ { 1 }$ and $R _ { 2 }$ are equivalence relations\\
(4) neither $R _ { 1 }$ nor $R _ { 2 }$ is an equivalence relation