Predicate Logic Flashcards by Ailsa Turner

Q

What are the De Morgans laws for quantifiers?

A

¬ (∀x.P(x)) ≡ ∃x.¬P(x)
¬ (∃x.P(x)) ≡ ∀x.¬P(x)

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Q

Is this true or false? ∀x∃y. Q(x,y) ≡ ∃x∀y.Q(x,y)

A

False

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Q

Is this true or false? ¬(∀x.P(x)) ≡ ∃x.¬P(x)

A

False

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Q

Is this true or false? ∀x∀y. Q(x,y) ≡ ∀y∀x. Q(x,y)

A

True

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Q

Is this true or false? ∀x.¬P(x) ≡ ∃x.¬P(x)

A

False

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