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Maths-

General

Easy

Question

Let $R$ be a relation on the set $N$ of natural numbers defined by $n R m left right double arrow n$ is a factor of $m open parentheses i. e. blank n blank close vertical bar blank m right parenthesis.$ Then, $R$ is

Reflexive and symmetric
Transitive and symmetric
Equivalence
Reflexive, transitive but not symmetric

The correct answer is: Reflexive, transitive but not symmetric

Since $n vertical line n$ for all $n element of N.$ Therefore, $R$ is reflexive. Since $2 vertical line 6$ but $6 ∤ 2 comma$ therefore $R$ is not symmetric
Let $n blank R blank m$ and $m blank R blank p$
$rightwards double arrow n blank R blank m$ and $m blank R blank p$
$rightwards double arrow n vertical line m$ and $m open vertical bar p rightwards double arrow n close vertical bar p rightwards double arrow n blank R blank p$
So, $R$ is transitive

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