Question

Let $R$ be a relation on the set $N$ of natural numbers denoted by $nRm \Leftrightarrow n$ is a factor of m (i.e. $n \,| \,m$). Then, $R$ is

• A. Reflexive and symmetric
• B. Transitive and symmetric
• C. Equivalence
• D. Reflexive, transitive but not symmetric

Answer 1

Answer: (D)

Reflexive, transitive but not symmetric

Answer 2

Reflexive : $n \, | \,n$ for all $n \in N$ $\Rightarrow R$ is reflexive. Symmetric : $2 | 6$ but $6 \, | \, 2$ $\Rightarrow R$ is not symmetric. Transitive : Let $nRm$ and $mRp$ $\Rightarrow n \,| \,m$ and $m|p$ $\Rightarrow n \,| \,p$ $\Rightarrow nRp$. So, $R$ is transitive.