Who invented $\vee$ and $\wedge$, $\forall$ and $\exists$?

See Earliest Uses of Symbols of Set Theory and Logic for this and much more.

The four types of propositions used in the classical Greek syllogisms were called A, E, I, O. Statements of type A were "All p are q". Statement of type E were "Some p are q". So of course a millennium later, mathematicians (who had a classical education) used A and E for these quantifiers, then later turned them upside down to avoid confusion with letters used for other things.

By the way: I and O were "All p are not q" = "No p are q" and "Some p are not q"="Not all p are q", but I don't remember which is I and which is O.