Ashley P.

asked • 10/08/19

Logic , Quantifiers , Logical Formula

Please note that I'll be using the following notations as follows, throughout the question.


VX - For all X (Universal Quantifier)

EX - For some X(Existential quantifier)


Consider the logic formulas G1 and G2 :

G1 : (VX)[ P(X) V Q(X) ] --> (VX)P(X) V (VX)Q(X)

G2 : (EX)P(X) --> (VX)P(X)


Can anyone please explain how do we obtain the intuitive meaning of G1 and G2 under the interpretation I over the set of integers ; under which


P(X) means that X is even and

Q(X) means that X is odd.

1 Expert Answer

By:

David G. answered • 10/10/19

Experienced Discrete Mathematics teacher and tutor

Ashley P.

Thanks for the response. But what do they tell about "obtaining the intutive meaning"? Does that mean we have to state whether the statement is either true or false or???
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10/12/19

David G.

tutor
Good point. I think what is desired for the intuitive meanings are what I wrote as G1 now becomes: "For all X, (X is odd or X is even) -> (For all X, X is odd) or (For all X, X is even)" and G2 now becomes: "There exists an integer X such that X is even -> For all integers X, X is even." I'm not sure whether you are also expected to say whether the statements are true or false. But I thought it was interesting to notice that both G1 and G2 were false.
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10/12/19

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