The two basic facts about the quantifiers you need to understand, and from which all of...

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Basic Math

The two basic facts about the quantifiers you need tounderstand, and from which all of the logical properties of thequantifiers follow are:
Basic Fact 1: A universal quantifier (x) Fx isequivalent to an infinite conjunction: Fa & Fb & Fc &Fd & ........
where a, b, c, d, are the names of objects in theuniverse picked out by the 'x' in the universal quantifier'(x)'.
Basic Fact 2: An existential quantifier is equivalent toan infinite disjunction
Fa v Fb v Fc v Fd v ......
Expand in a two-element universe
(a) ~(x) ((Fx v Gy) v Ka)

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Using a restricted universe of discourse to determine whether a given formula is true or false requires two additional bits of information a truth fractional expansionof the formula across the universe and an interpretation of the extension of the predicates used in the formula with respect to the elements in the universe A truthfunctional expansion of a See Answer

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