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Stuck on First-Order Logic

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#logic #predicate-logic #natural-deduction #formal-proofs
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An adequate difference between $\forall x\in A:P(x)$ and $(\forall x)(x\in A\rightarrow P(x))$?

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#predicate-logic #philosophy #first-order-logic #foundations #big-picture
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Is this assertion true or false? $(\exists x)(\exists y)(\forall z)(y \ne x+z \Rightarrow y\lt x)$ Cohn - Classic Algebra P7

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#logic #arithmetic #predicate-logic
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Proof using existential quantifier

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#logic #predicate-logic #quantifiers
112
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Give a formal derivation of ∃x~P(y) given the premises ~∃x(∀yP(y) ∧ Q(x)) and Q(b)

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#logic #predicate-logic
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How to express the number of subjects in a proposition by using predicates?

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#discrete-mathematics #logic #predicate-logic
239
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Is $\forall x [\exists y\ Q(x,y)\ \lor\ \forall z\ \neg Q(x,z)]$ valid?

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#logic #predicate-logic
402
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Logic question in Real Analysis

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#real-analysis #limits #logic #predicate-logic #higher-order-logic
218
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Logical problem in analysis

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#real-analysis #limits #logic #predicate-logic
67
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How do I interpret z in this equation?

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#discrete-mathematics #predicate-logic #quantifiers
1.7k
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Use predicates and quantifiers to express this statement.

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#logic #predicate-logic #quantifiers
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How are $ \exists x (P(x) ⊕ Q(x)) $ and $(\exists x P(x)) ⊕ (\exists x Q(x))$ not logically equivalent?

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#discrete-mathematics #predicate-logic #quantifiers
154
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Analyzing logical form of ∀x∀yM(x, y)

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#logic #predicate-logic #quantifiers
631
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First order theory - define a finite domain

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#order-theory #predicate-logic #first-order-logic
809
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First order theory - define a domain with an even number of elements

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#order-theory #predicate-logic #first-order-logic

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