Let R_{1} and R_{2} be two relations defined | vedclass

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Question

$R_{1}=\{x y \geq 0, x, y \in R\}$

For reflexive $x 	imes x \geq 0$ which is true.

For symmetric

If $x y \geq 0 \Rightarrow y x \geq 0$

I

Vedclass · Accepted Answer

neither $R_{1}$ nor $R_{2}$ is an equivalence relation

Vedclass · Answer

$R_{1}=\{x y \geq 0, x, y \in R\}$

For reflexive $x 	imes x \geq 0$ which is true.

For symmetric

If $x y \geq 0 \Rightarrow y x \geq 0$

If $x =2, y =0$ and $z =-2$

Then $x . y \geq 0 \& y . z \geq 0$ but $x . z \geq 0$ is not true $\Rightarrow$ not transitive relation.

$R_{ I }$ is not equivalence

$R _{2}$ if $a \geq b$ it does not implies $b \geq a$

$R_{2}$ is not equivalence relation

$D$

Let $R_{1}$ and $R_{2}$ be two relations defined on $R$ by $a R _{1} b \Leftrightarrow a b \geq 0$ and $a R_{2} b \Leftrightarrow a \geq b$, then

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