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Maths-

General

Easy

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
Reflexive and transitive
Symmetric and transitive
Equivalence relation

The correct answer is: Reflexive and transitive

For any integer $n comma$ we have
$n vertical line n rightwards double arrow n blank R blank n$
So, $n blank R blank n$ for all $n blank element of Z$
$rightwards double arrow R$ is reflexive
Now, $2 vertical line 6$ but 6 does not divide 2
$rightwards double arrow left parenthesis 2 comma blank 6 right parenthesis element of R$ but $left parenthesis 62 right parenthesis not an element of R$
So, $R$ is not symmetric
Let $left parenthesis m comma n right parenthesis element of R$ and $open parentheses n comma p close parentheses element of R.$ Then,
$open table row cell left parenthesis m comma n right parenthesis element of R rightwards double arrow m vertical line n end cell row cell left parenthesis n comma p right parenthesis element of R rightwards double arrow n vertical line p end cell end table close curly brackets rightwards double arrow m vertical line p rightwards double arrow left parenthesis m comma p right parenthesis element of R$
So, $R$ is transitive
Hence, $R$ is reflexive and transitive but it is not symmetric

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