Question

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

State the whether given statement is true or false

(i)$aRb⟺\left|a\right|=\left|b\right|$
it is Reflexive, not symmetric,transitive.

• A. True
• B. False

Answer 1

The correct option is B False

Given $aRb\iff |a|=|b|$
Reflexivity:
Since, $|a|=|a|$
$\Rightarrow aRa$
Hence, R is reflexive.
Symmetry:
Let $aRb$
$\Rightarrow |a|=|b|$
$or|b|=|a|$
$\Rightarrow bRa$
Hence, R is symmetric.
Transitivity:
Let $aRb,bRc$
$|a|=|b|;|b|=|c|$
$\Rightarrow |a|=|c|$
$\Rightarrow aRc$
Hence, R is transitive.