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why$(\forall x \in U, P(x)) \implies (\exists x \in U, P(x))$ is false?

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#logic #predicate-logic
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Is there any false case for that: $\exists x \in D, \forall y \in D, P(x, y) \implies P(y, x)$?

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#logic #predicate-logic
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Mathematical Predicate logic

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#graph-theory #predicate-logic
174
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$[\exists x \in U, P(x)] \implies [\forall x \in U, P(x)]$

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law of implication

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140
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Confused about the use of variables w/ logical quantifiers

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Proving the roots of a polynomial are irrational

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#logic #proof-writing #predicate-logic
167
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Are these two equivalences really as "immediate" as Jean-Yves Girard claims?

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#logic #predicate-logic
185
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Hierarchy of operators of propositional logic

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#logic #predicate-logic
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check the formulas for satisfiability and validity

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214
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prenex normal equivalence challenges in math

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#discrete-mathematics #logic #predicate-logic #first-order-logic
122
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sentence in predicate logic

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#logic #predicate-logic #first-order-logic
350
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$\forall$ At the beginning or at the end?

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#logic #notation #predicate-logic
64
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find a sentence $\alpha$ in some language L such that

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#logic #predicate-logic #first-order-logic
177
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proving{$\neg(\forall x)\alpha \rightarrow \alpha$}$\models$$(\forall x)\alpha$

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#logic #predicate-logic #first-order-logic #formal-proofs

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