Question

An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is

• A. Reflexive and symmetric
• B. Reflexive and transitive
• C. Symmetric and transitive
• D. Equivalence relation

Answer 1

Answer: (B)

Reflexive and transitive

Answer 2

For any integer n, we have $n \mid n \Rightarrow n R n$

So, for all $n \in Z \Rightarrow R$ is reflexive

Now 2|6 but 6+2,⇒ (2,6) $\in R$ but (6, 2) $\notin R$

So, R is not symmetric.

Let $( n , p ) \in R$.

Then

So, R is transitive.

Hence, R is reflexive and transitive but it is not symmetric.