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Is the “Empty String” a term in First Order Logic?

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136
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A 7-formula deduction for $\{\forall x (Px \to Qx), \forall z P z\} \vdash Qc$. Enderton logic page 123.

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956
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Metalanguage of mathematics

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74
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Understanding definable set

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#elementary-set-theory #relations #predicate-logic
58
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How to prove two statements are equivalent and give a counterexample if they're not.

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#discrete-mathematics #predicate-logic
71
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First-order logic from computational linguistics - implication

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#logic #first-order-logic #predicate-logic #mathematical-modeling #logic-translation
182
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Difference between $(\forall x A(x)) \implies (\forall x M(x))$ and $\forall x (A(x) \implies M(x))$

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#logic #predicate-logic #quantifiers
139
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Proving logical equivalences in the statements $(∃)(() → ())$ and $(∀)() → (∃)()$

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472
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Divisibility represented by Boolean logic

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#elementary-number-theory #predicate-logic #boolean-algebra #satisfiability
62
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Symbols of the language vs. Free variables

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#logic #predicate-logic #decidability #second-order-logic
564
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Does each variable in a premises undergoing Universal Instantiation have to change?

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#discrete-mathematics #logic #predicate-logic #quantifiers #logic-translation
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Does "P does not imply Q" mean that (P → Q) is not always true?

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#logic #proof-writing #propositional-calculus #predicate-logic #quantifiers
183
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Substitution Theorem on "A Concise Introduction to Mathematical Logic" by W. Rautenberg

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#logic #first-order-logic #predicate-logic #substitution
306
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Is there a proof of $\lnot \forall x, P(x) \iff \exists x, \lnot P(x)$

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65
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Translating set syntax in FOL

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