# Questions tagged [quantifiers]

The quantifiers $\forall$ ("for all") and $\exists$ ("there exists") distinguish predicate calculus from propositional logic.

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### Problem with Fitch : How to Eliminate ¬∃?

fitch problem: I've been working on a Fitch-style proof problem, and I've encountered a difficulty in a specific step (step 11). The problem restricts me to using Taut-Con rules from Con-Rules. Here’...
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### Counting the numbers of quantifiers, how are there 4?

From the book "Gentle Introduction to Art of Mathematics": How many quantifiers does this have and what kind? "Everybody has some friend that thinks they know everything about a sport.”...
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### Do the "nothing" and "unique existence" quantifiers respect or at least semi-respect ordered pairs?

Let $Nx$ be the quantifier "for no $x$", and let $\exists!x$ be the quantifier "there is one and only one $x$". Do those quantifiers respect ordered pairs? That is, is $NxNyP(x,y)$ ...
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### Particularization rules of premises with multiple quantifiers

I have this reasoning with multiple quantifiers and I need to prove it's validity $\exists x : [F(x) \wedge S(x)] \rightarrow \forall y : [M(y) \rightarrow W(y)]$ $\exists y : [M(y) \wedge \neg W(y)]$ ...
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