Let us define a relation R in R as aRb if a b. Then R is:

Question

Let us define a relation $R$ in $R$ as $a R b$ if $a \geq b$ . Then $R$ is:

Smart Achievers · Accepted Answer

(2)

Ans. Reflexive, transitive but not symmetric

Explanation:

Given that, $a R b if a \geq b$

$\Rightarrow a R a \Rightarrow a \geq a,$ which is true.

Hence, $R$ is reflexive.

Let $a R b$ , i.e., $a \geq b$ .

For symmetry, we require $b R a$ , i.e., $b \geq a,$ which is not true in general.

Hence, $R$ is not symmetric.

But if $a R b$ and $b R c$ ,

$\Rightarrow$ $a \geq b$ and $b \geq c$

$\Rightarrow$ $a \geq c$

Hence, $R$ is transitive.

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