I'm self-studying discrete mathematics and right now I'm reading a chapter about "Relations". I've tried to solve some of the exercises that are included at the end of the chapter. But they are too difficult to solve for me. Could you please give me a hint about this one?
Let $A$ be the set of all non-zero rational numbers. For all $a,b \in A$, let $R$ be a relation that is defined as follows:
$$ aRb \iff a|b\in\mathbb{Z} $$
Determine if $R$ is reflexive, transitive or symmetric.
I don't understand that "$\in \mathbb{Z}$" part. It was said earlier that $a$ and $b$ are non-zero rational numbers, but now it says that $b$ is an integer?
I presume it's a typo (or strange notation convention) and that what it is supposed to say is $$a\; R\; b\ \Leftrightarrow\ \frac{a}{b} \in \mathbb{Z}$$