Q:

What is the correct notation for the set of rational numbers $\frac{n}{m}$ with the constraint that $1\le n,m \le5$?

I have set that I want to neatly write down/present with set notation. The set contains: 
All the rational numbers $\frac{n}{m}$ with the constraint that $1\le n,m \le5, n,m\in \mathbb{Z}$.
I have come up with a few ways to write it down but I am not sure which one (if any) is correct.
$$\begin{align}
   \left\{ \frac{m}{n} \vert n,m\in \mathbb{Z} \land1\le n\le5 \land1\le m\le5\right\} \tag 1\\
   \left\{ \frac{m}{n} \in \mathbb{Q}\vert n,m\in \mathbb{Z} \land1\le n\le5 \land1\le m\le5\right\} \tag 2\\
  \left\{\frac{n}{m}\in \mathbb{Q}\vert n,m \in \mathbb{Z}, 1\le n,m\le 5\right\} \tag 3
\end{align}$$

A:

$(1)$ and $(2)$ are okay, though I would rather do it with $\frac{n}{m}$ instead of $\frac{m}{n}$.
In $(2)$ the part $\in\mathbb Q$ is redundant, but that does not harm correctness.
$(3)$ is wrong (e.g. it demands that $m\leq1$)

Actually you cannot speak of "the" correct notation of..., but of "a" correct notation of...

