Question

An integer $m$is said to be related to another integer $n$if m is a multiple of $n$then the relation is

• A. $Reflexiveandsymmetric$
• B. $Reflexiveandtransitive$
• C. $Symmetricandtransitive$
• D. $Equivalencerelation$

Answer 1

The correct option is B

$Reflexiveandtransitive$

Explanation for the correct option:

Given, $mRn$ means $m$is said to be related to another integer $n$ i.e. if $m$ is a multiple of $n,n,m\in I$

That is $mRnifn=km$ where $m,n,k$ are integers.

Now since, the multiple of every numbers is number also

That is $n=1\times n\forall n\in I$

Hence, $R$ is reflexive.

$R$ is not symmetric as $6$ is a multiple of $2$ but $2$ is not a multiple of $6$.

Now, transitivity

Let $mRn,nRp$ then,

$\Rightarrow m=k_{1}nandn=k_{2}pwhere{k}_{1,}{k}_{2,,}p\in I$

$\Rightarrow m=k_1{k}_{2}p$

$\Rightarrow m=kp$where $k=k_1{k}_2$

Hence,$m$ is a multiple of $P$

Hence , R is transitive

Hence option $\left(B\right)$ is correct.