Question

Let us define a relation $R$ in $R$ as $aRb$ if $a\ge b$. Then $R$ is

• A. an equivalence relation
• B. reflexive, transitive but not symmetric
• C. symmetric, transitive but
• D. neither transitive nor reflexive but symmetric

Answer 1

The correct option is B reflexive, transitive but not symmetric

Given that $aRb$ is $a\ge b$
$\Rightarrow aRa\Rightarrow a\ge a$ which is true
let $aRb,a\ge b$, theb $b\ge a$ which is not true $R$ is not symmetric.
But $aRb$ and $bRc$
$\Rightarrow a\ge b$ and $b\ge c$
$\Rightarrow a\ge c$
Hence, $R$ is transitive.