Question

Let R be a relation on the set N of natural numbers defined by nRm

⇔ 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 n $in$ N,

therefore R is reflexive.

Since 2 | 6 but 6 | 2, therefore R is not symmetric.

Let n R m and m R p $\Rightarrow$ n|m and m|p $\Rightarrow$ n|p $\Rightarrow$ nRp

So. R is transitive.