Mathematics, 24.08.2020 01:01 92terbes

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)))

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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)))

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Another question on Mathematics

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)))