The Existential Quantifier, usually written as a back-to-front capital E indicates the existence of a thing of a certain sort satisfying certain conditions. The Universal Quantifier, usually written as an upside-down capital A, indicates that every thing of a certain sort satisfies those conditions.
all, none, some, or not all of something is what your going to deal with mostly. the hardest thing for me is translation into PD (predicate logic). upside down capital A "∀" means for everything in the universe of discourse you are tramslating. example : all Greeks are human (∀x) (Gx > Hx) "for all x, if x is greek, then x is human" this basically means the universe of discourse is Greeks (for all G basically). now this ∀ symbol is called a quantifier. it is a universal quantifier... hence for "ALL" x now there is another quantifier. an existential quantifier. this is different from universal because it is not for every x, it is for AT LEAST ONE (which means there is an x) or not all x. this symbol is a backwards E "∃" example: there is a greek that is human (∃x) (Gx & Hx) "there exists an x, (such that, or and) x is greek and x is human" notice that the universal is a "if, then" or (>) statement and the existential is a "&" statement. for the most part this is how they work but there are some instances were both can be implemented... example: all greek athelete's are human (∀x) (Gx & Ax) > Hx "for all x, if x is a greek and an athelete, then x is a human" this is mostly predicate stuff but hopefully a good start to the harder stuff young blood.
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