Kenneth Rosen Edition 6th Exercise 1.4 Question 8 (Page No. 58)

Question

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.

Comments

$\exists x\exists y \left ( x \neq y \wedge Q(x, jeopardy) \wedge Q(y, jeopardy) \right )$

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Here y is indicating quiz show name . So , how it can be Q(y,jeopardy) and jeopardy itself is a tv show. Pls elaborate it .

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x and y used to represent two student since there no need to use quantifier on quiz name(only one quiz is there with name if it ask atleast one quiz then it used with quantifier).

Answer 1

hope it helps!

Answer 2

a. ∃x ∃y Q(x, y)
b. ∃x ∃y ¬Q(x, y)
c. ∃x (Q(x, Jeopardy) ∧ Q(x, Wheel of Fortune))
d. ∀y ∃x Q(x, y)
e. ∃x ∃y ((x != y) ∧ Q(x, Jeopardy) ∧ Q(y, Jeopardy))