0
votes
1answer
41 views

Nested Quantifiers - Differentiating between $\forall x \forall y$, $\forall x \exists y$, and $\exists x \exists y$

I have a few questions regarding quantifiers which I'm still not clear about. 1) $\forall x \forall y (x^2 + y^2 = 9)$ I believe this is false as x and y could be 2 and results in 8. 2) $\forall x ...
1
vote
2answers
36 views

Propositional logic-Predicates

I have this problem in my Discrete structures course Show why : ∀x P(x) ∨∀x Q(x) is not logically equivalent to ∀x(P(x)∨Q(x)) . Please help solve this
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2answers
203 views

Is double quantifying a variable possible in predicate logic?

I read it as "Everyone is either a student or has read every book". But what's the use of the existential y outside the bracket? ...
-1
votes
1answer
125 views

Stuck on proving demorgans with quantifiers [closed]

What I'm trying to prove, using propositional and quantifier rules, is $$\neg \exists{x} \; A(x) \iff \forall{x} \; \neg A(x).$$ So far, I've only started proving it left to the right, and I'm ...