Question

For $n, m \in N, n \mid m$ means that $n$ is a factor of $m$, then prove that relation | is reflexive, transitive but not symmetric.

Answer 1

$n R m \Rightarrow n$ is factor of $m$

(i) $R$ is reflexive

(ii) $R$ is not symmetric because $\frac{m}{n}=K$ but $\frac{n}{m} \notin N$

(iii) $R$ is transitive.