Question

If $n|m$ means that $n$ is a factor of $m$, the relation $"|"$ is

• A. Reflexive and symmetric
• B. Transitive and symmetric
• C. Reflexive, transitive and symmetric
• D. Reflexive, transitive and not symmetric

Answer 1

The correct option is D Reflexive, transitive and not symmetric

$R=\{(n,m):n|m,meansnisthefactorofm\}$

$\left(i\right)$For reflexive,

$(a,a)\in R$

for this $a$ should be the factor of a which is true and hence the relation is reflexive

$\left(ii\right)$For symmetric,

If $n,m\in R$

then $m,n$ and should also be in $R$ but cannot be happening

so, the relation is not symmetric

For example $3$ is the factor of $6$ but $6$ is not the factor of $3$

$\left(iii\right)$ For transitive ,

if $n,m\in R$

and $m,l\in R$

then automatically $n,l\in R$

$\therefore$relation is transitive

Hence the relation is reflexive and transitive but not symmetric