How to translate sentences to predicate logic?

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Here are the sentences I worked on, I am unsure of my formulations and was wondering if I can get some feedback.

Unicorns do not exist.

$\forall x, \neg unicorn(x)$

Every professional tennis player could beat any amateur tennis player.

$\forall x \forall y (professional(x) \land amateur(y) \rightarrow beat(x,y) ) $