TITLE: Existential Quantifiers translated into categorical statements?
QUESTION [1 upvotes]: I've been recently trying to translate the categorical statements into the quantifiers ($\forall$ and $\exists$). 
Attempts
I believe I can make the E statement as $$\nexists s:p,$$the A statement as $$\neg\nexists s:p,$$ the I statement as $$\exists s:p,$$
and the O statement as $$\neg\exists s:p.$$
Question
Are my formulas correct? If not, how might I translate the categorical statements correctly?

REPLY [2 votes]: Here is the way I would do it in AEIO order:
$$\forall x:S(x)\implies P(x)$$
$$\forall x:S(x)\implies \neg P(x)$$
$$\exists x:S(x)\wedge P(x)$$
$$\exists x:S(x)\wedge \neg P(x)$$
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