I am trying to prove or disprove the statement:
$\mathcal{U} = \mathbb{R} > 0$
$\exists x \forall y [xy = 1]$
However, I have not learned the rule on how to do so. Does it somehow follow the single quantifier rule where: $\forall x [p(x)]$ changes to $ \exists x [ \neg p(x) ] $ ?
I am only looking for rule on how to solve this, not the solution. Can anyone enlighten me?