Question

Let R be a relation on the set N of natural numbers defined by $nRm\iff n$ 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, transitive but not symmetric

Since n | n for all $nϵN$, therefore R is reflexive. Since 2 | 6 but $6\text{/}|2$, therefore R is not symmetric.
Let n R m and $mRp\Rightarrow n|mandm|p\Rightarrow n|p\Rightarrow nRp$. So, R is transitive.