A relation R is defined on the set of natural | vedclass

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(B) Let $A$ be the set of natural numbers. The relation $R$ is defined as $m R n$ if $m$ is a multiple of $n$,i.e.,$m = kn$ for some $k \in \mathbb{N}

Vedclass · Accepted Answer

Reflexive and transitive

Vedclass · Answer

(B) Let $A$ be the set of natural numbers. The relation $R$ is defined as $m R n$ if $m$ is a multiple of $n$,i.e.,$m = kn$ for some $k \in \mathbb{N}$.$1$. Reflexive: For any $m \in A$,$m = 1 	imes m$,so $m$ is a multiple of $m$. Thus,$(m, m) \in R$. The relation is reflexive.$2$. Symmetric: If $(m, n) \in R$,then $m = kn$. This does not imply $n = k'm$ for $m 
eq n$. For example,$4$ is a multiple of $2$,but $2$ is not a multiple of $4$. Thus,the relation is not symmetric.$3$. Transitive: If $(m, n) \in R$ and $(n, p) \in R$,then $m = kn$ and $n = lp$ for some $k, l \in \mathbb{N}$. Substituting $n$,we get $m = k(lp) = (kl)p$. Since $kl \in \mathbb{N}$,$m$ is a multiple of $p$. Thus,$(m, p) \in R$. The relation is transitive.Therefore,the relation is reflexive and transitive.

$A$ relation $R$ is defined on the set of natural numbers such that $m$ is related to $n$ if $m$ is a multiple of $n$. Then the relation is:

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