Kenneth Rosen Edition 7 Exercise 1.5 Question 4 (Page No. 64)

Question

Let $P(x, y)$ be the statement “Student $x$ has taken classy,” where the domain for $x$ consists of all students in your class and for $y$ consists of all computer science courses at your school. Express each of these quantifications in English.

1. $\exists x \exists y P(x,y)$
2. $\exists x \forall y P(x,y)$
3. $\forall x \exists y P(x,y)$
4. $\exists y \exists x P(x,y)$
5. $\forall y \exists x P(x,y)$
6. $\forall x \forall y P(x,y)$