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

Answer: (D)

Reflexive, transitive but not symmetric

Answer 2

Since n | n for all $n \in N$, therefore R is reflexive. Since 2 | 6 but $6 \mid 2$, therefore R is not symmetric.

Let n R m and m R p ⇒ n|m and m|p ⇒ n|p ⇒ nRp. So R is transitive.