Sets , Relations , Functions - 2

Probability Level 1

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

Reflexive and Transitive Symmetric and Transitive Symmetric only Equivalence relation Reflexive only Transitive only Reflexive and Symmetric

1 solution

Gagan Raj
Apr 14, 2015

For any integer $n$ , we have $n|n$ is $nRn$ . So $nRn$ for all $n\in{Z}$ .

Thus , R is reflexive. (R is the relation)

Now , $(2,6)\in{R}$ but $(6,2)$ $does~not$ $\in{R}$

So , R is not symmetric .

Let $(m,n)\in{R}$ and $(n,p)\in{R}$

Then , $(m,p)\in{R}$

So , R is transitive .

Hence , R is reflexive and transitive but not symmetric .