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 and symmetric
• B. reflexive and transitive
• C. symmetric and transitive
• D. an equivalence relation

Answer 1

Answer: (B)

For any integer $n$, we have $n/n\Rightarrow nRn$
So, $nRn$ for all $n\in Z\Rightarrow R$ is reflexive.
Now, $2/6$ but $6+2\Rightarrow (2,6)\in R$ but $(6,2)\notin R$
So, $R$ is not symmetric.
Let $(m,n)\in R$ and $(n,p)\in R$

So, $R$ is transitive. Hence, $R$ is reflexive and transitive but it is not symmetric.