Let Q(x,y) be the statement “x has been a contestant on quiz show y”, where the domain of x is the set of students and the domain for y consists of all quiz shows. For each of the English sentences below, please express it in terms of $Q(x,y)$ with quantifiers.
Please Correct me:
(i) Alice has never appeared in Jeopardy. $\quad\exists x \exists y \neg Q(x,y) $
(ii) Every quiz show has had a student as a contestant. $\quad \forall y \exists x Q(x,y)$
(iii) No student has appeared in both Wheel of Fortune and Family Feud:
- $\neg \exists x_1\neg \exists x_2 Q((x_1, \text{Wheel of Fortune}) \land \exists x_2 Q(x_2, \text{Family Feud}))$