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section * { Problem 2 } Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences:
sectionProblem
Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences:
beginenumeratelabelalph
item $
eg forall x leftPxland
eg Qxright; equiv ; exists x left
eg Pxlor Qxright$
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item $
eg forall x left
eg Pxto Qxright; equiv ; exists x left
eg Pxland
eg Qxright$
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item $
eg exists x big
eg Pxlor leftQxland
eg Rxrightbig; equiv ; forall x big Pxland left
eg Qxlor Rxrightbig$
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endenumerate
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