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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.

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    Thanks I'm always confused as what I should tag some of these with. Oh also if you guys want to put your suggestions as an answer then I could accept it.2012-07-06

1 Answers 1

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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.