Assume that ∀x∃yP(x, y) is false and the domain of them is nonempty. Which of the following must be false? (i) ∀x∀yP(x, y) (ii) ∃x∀yP(x, y) (iii) ∃x∃yP(x, y)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 36E
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Assume that ∀x∃yP(x, y) is false and the domain of them is nonempty. Which of the following

must be false?

(i) ∀x∀yP(x, y)

(ii) ∃x∀yP(x, y)

(iii) ∃x∃yP(x, y)

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