Give interpretations to prove that each of the following wffs is not valid. (a) (∀x)(∃y)P(x, y) → (∃x)(∀y)P(x, y) (b) (∀x)[P(x) → Q(x)] → [(∃x)P(x) → (∀x)Q(x)] (c) (∀x)[A(x)]' ↔ [(∀x)A(x)]'

Give interpretations to prove that each of the following wffs is not valid. (a) (∀x)(∃y)P(x, y) → (∃x)(∀y)P(x, y) (b) (∀x)[P(x) → Q(x)] → [(∃x)P(x) → (∀x)Q(x)] (c) (∀x)[A(x)]' ↔ [(∀x)A(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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Question

Give interpretations to prove that each of the following wffs is not valid.
(a) (∀x)(∃y)P(x, y) → (∃x)(∀y)P(x, y)
(b) (∀x)[P(x) → Q(x)] → [(∃x)P(x) → (∀x)Q(x)]
(c) (∀x)[A(x)]' ↔ [(∀x)A(x)]'

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