I have a homework question that asks me to determine determine whether given relations are reflexive, symmetric, anti-symmetric, asymmetric or transitive.
One relation is:
$\rho \subseteq \mathbb \times \mathbb Z$, where $a~\rho~b$ if and only if there is $n \in \mathbb Z$ such that $a = bn$
The answer says it's reflexive and transitive. How come is it not anti-symmetric?
We only find $x~\rho~y$ and $y~\rho~x$ if $x = y$.
like in (1,1) or (2,2).