Question

The following relation is defined on the set of real number:

State the whether given statement is true or false

(ii)$aRb⟺\left|a\right|\ge \left|b\right|$
The following relation is
(Reflexive,not symmetric, transitive.

• A. True
• B. False

Answer 1

The correct option is A True

Let $aRb\iff |a|\ge |b|$
Reflexivity:
We can write $|a|\ge |a|$ (As every number is greater or equal to itself.)
$\Rightarrow aRa$
Hence, R is reflexive.
Symmetry:
Let $aRb$
$\Rightarrow |a|\ge |b|$
We cannot write this as $|b|\ge |a|$
Hence, $b$ is not related to $a$
Hence, R is not symmetric.
Transitivity:
Let $aRb,bRc$
$\Rightarrow |a|\ge |b|;|b|\ge |c|$
$\Rightarrow |a|\ge |c|$
$\Rightarrow aRc$
Hence, R is transitive.