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

The Correct Option is D

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.