1.5 Quantifiers & Predicate Logic | 1.5 Quantifiers & Predicate Logic | Unit 1: Proofs | Mathematics for Computer Science | Electrical Engineering and Computer Science

Quantifiers

Let $Q(x,y)$ be the statement

" $x$ has been a contestant on television show $y$ ."

The domain of discourse for $x$ is the set of all students at your school and for $y$ is the set of all quiz shows on television.

Which of the following are logically equivalent to:

"No student at your school has ever been a contestant on a television quiz show."

$\forall x \forall y . \text{NOT}(Q(x,y))$

$\exists x \exists y. \text{NOT}(Q(x,y))$

$\text{NOT}(\forall x \forall y . Q(x,y))$

$\text{NOT}(\exists x \exists y . Q(x,y))$