Given any two rational numbers $a$ and $b$, it follows that $ab$ is rational.
$\forall$$a$,$b$ $s.t.$ (($a$,$b$ $\in$ $\mathbb{Q}$) $\implies$ ($a$$b$ $\in$ $\mathbb{Q}$))
But I've seen it written:
$\forall$$a$,$b$ $\in$ $\mathbb{Q}$ $s.t.$ ($a$$b$ $\in$ $\mathbb{Q}$)
The second reads as "for all rational $a$ and $b$ such that $ab$ is rational". Obviously this does not parse well, and for the same reason, I would argue the first one is flawed too.
Here are two standard alternatives: $$ \forall a,b\left[\left(\left(a,b\in\mathbb{Q}\right)\implies\left(ab\in\mathbb{Q}\right)\right)\right] \hspace{4em}\text{or}\hspace{4em} \forall a,b\in \mathbb{Q}\left[ ab\in\mathbb{Q}\right]. $$