Is my answer to question 1 correct or is the double ∃ mean each student has taken each CS class?
Let P(x, y) be the statement “Student x has taken class y,” 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) ∃x∃yP(x, y)
2) ∃x∀yP(x, y)
1) There exists a student that has taken one CS class.
2) There exists a student that has taken all CS classes.
Edit: New answers based on suggestions. 1) At least one student has taken at least one CS class. 2) At least one student has taken all CS classes.