# Symbolic Logic Problem

Use the method of truth table expansion to determine whether or not the sentence below is a theorem of quantified logic. The # indicates a biconditional, usually indicated by a double arrow.

(EX)(Y)FXY#(Y)(EX)FXY

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#### Solution Preview

I am assuming that (EX) is the existential quantifier "There exists an x such that..." and that (Y) is the universal quantifer "For all Y the following holds..."

The trick is to pick a small finite universe, such as one with two elements A and B.

Then the expresion (EX)FX expands to FA v FB ( here I use "v" for logical or")

That is, for a unverse of two elements, if there exists an x such that the predicate F about x is true, this can only be the case if the predicate F is true for either the first element A or the second element B. Another way of saying this is that applying the existential quantifier to an expression is the same as applying to the "or" operation between each possible value of the ...

#### Solution Summary

The validity of a symbolic logic expression is investigated. A method of truth table expansions are used.