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."

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

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

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

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