Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences: (a) x (P(x)^-Q(x)) = 3x (-P(x) v Q(x)) (b) x (P(x)→→ Q(x)) = 3x (-P(x) ^ ¬Q(x)) (c) -3x (-P(x) v (Q(x) ^-R(x))) = x (P(x) ^ (-Q(x) v R(x)))
Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences: (a) x (P(x)^-Q(x)) = 3x (-P(x) v Q(x)) (b) x (P(x)→→ Q(x)) = 3x (-P(x) ^ ¬Q(x)) (c) -3x (-P(x) v (Q(x) ^-R(x))) = x (P(x) ^ (-Q(x) v R(x)))
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![EXERCISE 1.8.4: Using De Morgan's law for quantified statements to prove logical equivalence.
Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences:
(a) x (P(X)^-Q(x)) = 3x (-P(x) v Q(x))
(b)
x (P(x)→ Q(x)) = 3x (-P(x) ^ -Q(x))
(c) -3x (-P(x) v (Q(x) A-R(x))) = x (P(x)^(-Q(x) v R(x)))](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F321729d8-08c4-4111-ad0c-0f375c5ded4e%2F4db3d6c9-4b8f-4798-9987-7d62d5f043ad%2Fbcbdo3s_processed.png&w=3840&q=75)
Transcribed Image Text:EXERCISE 1.8.4: Using De Morgan's law for quantified statements to prove logical equivalence.
Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences:
(a) x (P(X)^-Q(x)) = 3x (-P(x) v Q(x))
(b)
x (P(x)→ Q(x)) = 3x (-P(x) ^ -Q(x))
(c) -3x (-P(x) v (Q(x) A-R(x))) = x (P(x)^(-Q(x) v R(x)))
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