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. Reflexive & Symmetric
• B. Reflexive and Transitive
• C. Symmetric and Transitive
• D. Equivalence Relation

Answer 1

The correct option is B

Reflexive and Transitive

Explanation for correct option.

Step1. For reflexive relation

Given, An integer $m$ is said to be related to another integer $n$ if $m$ is a multiple of $n$.

$\because (m,m)\in R,(n,n)\in R$

$R$ is reflexive.

Step2. For symmetric.

$(2,6)\in R,(m,n)\in R,$but $(6,2)\notin R$,

$R$ is not symmetric.

Step3. Relation is transitive.

$$\begin{gathered} (m,n)\in R \\ \Rightarrow \left(\frac{m}{n}\right) \end{gathered}$$

$$\begin{gathered} (n,p)\in R \\ \Rightarrow \left(\frac{n}{p}\right) \end{gathered}$$

So, $(m,p)\in R$

$R$ is transitive.

Hence, correct option is $\mathbf{\left(}\mathbf{B}\mathbf{\right)}$