I'm studying discrete mathematics now and I have trouble solving this question. The question is the next line.
Let $Q(x,y)$ be the statement "student $x$ has been a contestant on quiz show $y$". Express each of these sentences in terms of $Q(x,y)$, quantifiers, and logical connectives, where the domain for $x$ consists of all students at your school and for $y$ consists of all quiz shows on television.
a) There is a student at your school who has been a contestant on a television quiz show.
b) No student at your school has ever been a contestant on a television quiz show.
c) There is a student at your school who has been a contestant on Jeopardy and on Wheel of Fortune.
d) Every television quiz show has had a student from your school as a contestant.
e) At least two students from your school have been contestants on Jeopardy.
and I thought
a) should be $\exists\, x \exists\, y(Q(x,y))$
b) should be $\lnot\exists\, x(\exists\, y(Q(x,y)))$
d) should be $\forall\, y(\exists\, x(Q(x,y)))$
and I don't know how to solve c), e).
I want to check my answers are right and solve c), e). I need your help.
The answers you have given are correct.
For the ones you can't solve, you need to realize that $Q(x,y)$ is a function, and you can substitute for the variables. For example to express "John has been of a quiz show," we would say, $\exists y(Q(John,y))$
Now I'm sure you'll be able to do the other two.
BTW, please look at how I edited your question. You should use MathJax to format questions on this site.