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## Consider the first-order logic sentence φ ≡ ∃s∃t∃u∀v∀w∀x∀y ψ(s,t, u, v, w, x, y) where ψ(s,t, u, v, w, x, y) is a quantifier-free first-order logic formula using only predicate symbols, and possibly equality, but no function symbols. Suppose φ has a model with a universe containing 7 elements. Which one of the following statements is necessarily true?

Asked On2019-05-29 11:21:55 by:vivekEdu

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- A.Quick logic review -

Isα $\alpha $ true for domain ofx $x$, I can always give you y $y$ that is less than your number x $x$.

all integers?, Yes it is true. You pick any numberIsα $\alpha $ true for domain of{0,1,2,3,…} $\{0,1,2,3,\dots \}$ ? No, it is not true. (You pick any number x $x$) If you pick 0 $0$ then I can not give you y $y$ which is less than 0 $0$.

Non Negative integersDefinition ofModel $\text{Model}$ - α $\alpha $,

Domainfor which my sentence is true. For above sentenceall integersis model and there can be many other models, like -real numbers.(Definition ofCo Model $\text{Co Model}$-

Domainfor which my sentence is False.)Likes:

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