Answer
a) $\exists x \exists y Q(x,y)$
b) $\forall x \forall y \neg Q(x,y)$
c) $\exists x Q(x, Jeopardy) \land Q(x, Wheel of fortune)$
d) $\forall y \exists x Q(x,y)$
e) $\exists x \exists z((x\ne y) \land Q(x, Jeopardy) \land Q(z, Jeopardy))$
Work Step by Step
a) There is a student at your school who has been a contestant
on a television quiz show
$\exists x \exists y Q(x,y)$
b) No student at your school has ever been a contestant
on a television quiz show.
$\forall x \forall y \neg Q(x,y)$
c) There is a student at your school who has been a contestant
on Jeopardy and on Wheel of Fortune.
$\exists x Q(x, Jeopardy) \land Q(x, Wheel of fortune)$
d) Every television quiz show has had a student from
your school as a contestant.
$\forall y \exists x Q(x,y)$
e) At least two students from your school have been contestants
on Jeopardy.
$\exists x \exists z((x\ne y) \land Q(x, Jeopardy) \land Q(z, Jeopardy))$
