Question

For $n,m\in N$, $n|m$ 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

Since $n$ is a factor of $n$, so the relation is reflexive.

It however $n$ is a factor of $m$, $m$ is not necessarily a factor of $n$,

So the relation is not symmetric.

On the other hand $n|m$ and $m|0$ imply $n|0$,

So the relation is transitive.