Which of the following is a logical equivalence in first-order logic? A. ¬(∀x)P(x) ≡ (∃x)¬P(x)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 56E
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Which of the following is a logical equivalence in first-order logic?

A. ¬(∀x)P(x) ≡ (∃x)¬P(x)

B. (∀x)(∃y)P(x, y) ≡ (∃y)(∀x)P(x, y)

C. (∀x)(P(x) → Q(x)) ≡ (∃x)(P(x) ∧ Q(x))

D. (∀x)(P(x) ∧ Q(x)) ≡ (∀x)(P(x) ∨ Q(x))

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