Question

Prove the following theorems in $\mathscr{N}$ : $\mathbf{.} \sim \exists \mathbf{x} \mathbf{A} \equiv \forall \mathbf{x} \sim \mathbf{A}$.

   Prove the following theorems in $\mathscr{N}$ :
$\mathbf{.} \sim \exists \mathbf{x} \mathbf{A} \equiv \forall \mathbf{x} \sim \mathbf{A}$.

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Computer Science & Applied Mathematics)

An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Computer Science & Applied Mathematics)

Peter B. Andrews 1st Edition

Chapter 3, Problem 2

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The statement $\sim \exists \mathbf{x} \mathbf{A} \equiv \forall \mathbf{x} \sim \mathbf{A}$ asserts that the negation of the existence of an element $\mathbf{x}$ for which the statement $\mathbf{A}$ holds is equivalent to stating that for all elements Show more…

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Prove the following theorems in $\mathscr{N}$ : $\mathbf{.} \sim \exists \mathbf{x} \mathbf{A} \equiv \forall \mathbf{x} \sim \mathbf{A}$.

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