# [SOLVED]check if relation is equivalent

#### issacnewton

##### Member
Hello

I have to check if the following relation is an equivalence relation.
$m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0$

I think this relation fails to be reflexive since $(0,0)$ does not belong to
this relation. Hence this is not an equivalent relation. Is this ok ?

Thanks

#### caffeinemachine

##### Well-known member
MHB Math Scholar
Hello

I have to check if the following relation is an equivalence relation.
$m\sim n \;\;\mbox{in}\;\;\mathbb{Z}\;\;\mbox{if}\; mn > 0$

I think this relation fails to be reflexive since $(0,0)$ does not belong to
this relation. Hence this is not an equivalent relation. Is this ok ?

Thanks
Yes. This is good.