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Logical implications between $\forall x (P(x) \to Q(x))$ and $\forall x P(x) \to \forall x Q(x)$

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#propositional-calculus #predicate-logic
234
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Truth trees and validity

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#logic #predicate-logic
470
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How to show that a predicate logic formula's satisfiability is undecidable?

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#predicate-logic #satisfiability
58
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Help proving $odd(m^2+n^2) \implies odd((m+n)^2)$

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#proof-writing #predicate-logic
107
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Help proving $\text{odd}(m^2-n^2)\implies \text{odd}((m+n)^2)$

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#elementary-number-theory #logic #proof-writing #predicate-logic
2.5k
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Proofs with floor and ceiling: $\lceil -x \rceil = -\lfloor x \rfloor$

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#logic #proof-writing #predicate-logic #ceiling-and-floor-functions
789
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Discrete Math and about domain of discourse

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#predicate-logic
63
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Logical structure of $ (\forall x\ \mathsf{P}(x)) \implies \mathsf{Q}$, with $x$ absent from $\mathsf{Q}$

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#predicate-logic
363
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Is this a valid or invalid inference?

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#logic #predicate-logic #first-order-logic
59
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Application of Conditionals to Sets

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#logic #propositional-calculus #predicate-logic #quantifiers
61
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How to state uniqueness mathematically using predicates?

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#discrete-mathematics #predicate-logic
125
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Prove $q \lor r \vdash (q \land s) \lor (s \to r)$ using natural deduction

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#logic #propositional-calculus #predicate-logic #natural-deduction
773
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Restrictions on the use of universal generalization

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#logic #predicate-logic #first-order-logic #natural-deduction
99
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Translation into predicate calculus

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#logic #predicate-logic #logic-translation
349
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Translating to predicate logic

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#logic #predicate-logic #logic-translation

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