Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is:

Question

Let R be a relation on the set N of natural numbers defined by $n R m$ if $n$ divides $m$ . Then R is:

Smart Achievers · Accepted Answer

(4)

Ans. Reflexive, transitive but not symmetric

Explanation:

Since $m$ divides $n, \forall n \in N, R$ is reflexive. $R$ is not symmetric since for $3, 6 \in N, 3 R 6 \neq 6 R 3$ .

$R$ is transitive since for $n, m, r$ , whenever $\frac{n}{m}$ and $\frac{m}{r}$ $\Rightarrow \frac{n}{r},$ i.e., $n$ divides $m$ and $m$ divides $r$ , then $n$ will divide $r$ .

Solution

Q.
Let R be a relation on the set N of natural numbers defined by $n R m$ if $n$ divides $m$ . Then R is:

1 Reflexive and symmetric

2 Transitive and symmetric

3 Equivalence

4 Reflexive, transitive but not symmetric

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