Show that the statement (Væ P(x)) V (Væ Q(x)) → Vx (P(x) V Q(x)) is a tautology. Show that its converse is not a tautology by giving a counterexample.

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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Show that the statement
(Vx P(x)) V (Væ Q(x)) → Væ (P(x) V Q(x))
is a tautology. Show that its converse is not a tautology by giving a counterexample.
Transcribed Image Text:Show that the statement (Vx P(x)) V (Væ Q(x)) → Væ (P(x) V Q(x)) is a tautology. Show that its converse is not a tautology by giving a counterexample.
Show that the statement
(Vx P(x)) V (Væ Q(x)) → Væ (P(x) V Q(x))
is a tautology. Show that its converse is not a tautology by giving a counterexample.
Transcribed Image Text:Show that the statement (Vx P(x)) V (Væ Q(x)) → Væ (P(x) V Q(x)) is a tautology. Show that its converse is not a tautology by giving a counterexample.
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