Tagged Questions
5
votes
6answers
568 views
Confused between Nested Quantifiers
I am reading nested quantifiers. I am confused in between two cases,
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3
votes
4answers
146 views
Quantifies, predicates, logical equivalence
I am asked if $(\exists x) (P(x) \rightarrow Q(x))$ and $\forall x P(x) \rightarrow \exists xQ(x)$ are logically equivalent. I dont think they are but how will I prove it. Am I supposed to use either ...
2
votes
2answers
91 views
Are these two predicate statements equivalent or not?
$\exists x \forall y P(x,y) \equiv \forall y \exists x P(x,y)$
I was told they were not, but I don't see how it can be true.
7
votes
4answers
466 views
Why is the “finitely many” quantifier not definable in First Order Logic?
In First Order Logic with Identity (FOL+I), one can express the proposition that there are exactly 3 items that have the property P.
Why is it not possible to express the proposition that there is a ...
11
votes
10answers
475 views
Quantifier Notation
What's the difference between $\forall \space x \space \exists \space y$ and $\exists \space y \space \forall \space x$ ? I don't believe they mean the same thing even though the quantifiers are ...
2
votes
3answers
120 views
Are these two statement equivalent?
$\forall x \exists y P(x,y)$
$\exists x \forall y P(x,y)$
where P(x,y) means x is smaller than y.
I believe that they mean the same thing.
2
votes
5answers
436 views
How can I get the negation of $\exists!$ (unique existential quantification)?
How can I get the negation of $\exists!$ (unique existential quantification)? if it's $\forall$, So if I wanna re-negate the last one, I'll get $\exists$ but it's not the same as what we started with! ...
1
vote
2answers
104 views
Restrictions on universal specification (in first-order logic)?
I'm currently working my way through the details of first-order logic (using Suppe's Introduction to Logic), and I have a question about universal specification (US) (aka universal instantiation or ...
1
vote
2answers
168 views
interpreting mixed quantifier
I want to interpret the below sentences...
∀x∃y(Cube(x) → (Tet(y) ∧ LeftOf(x, y)))
∃y∀x (Cube(x) → (Tet(y) ∧ LeftOf(x, y)))
Actually I could interpret the first sentence.
Meaning: Every Cube is ...
