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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)) x(¬P (x) Q(x))∀∧≡∃∨
b) ¬ x(¬P (x) = Q(x)) x(¬P (x) ¬Q(x))∀⇒≡∃∧
c) ¬ x(¬P (x) (Q(x) ¬R(x))) x(P (x) (¬Q(x) R(x)))

Respuesta :

batolisis

Answer:

A) ¬(¬q) ≡ q

B) ≡ ( эx) (¬p(x) ∧ ¬q(x)

C) ≡ ( зx ) (p(x) ∧ (¬ q(x) ∨ r(x)) )

Step-by-step explanation:

using De Morgan's law for quantified statements and the laws of propositional logic to show the equivalent of the following

from De -Morgan law

¬(A ∨ B ) = ¬ A ∧¬ B

ATTACHED BELOW IS THE COMPLETE SOLUTION

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