Suppose the variable x represents the students, y represents courses, and (x, y) means "x is taking y ". Match each sentence to one or more logical statements.

(1) Every course is being taken by at least one student.
(2) Some student is taking every course.
(3) No student is taking all courses.
(4) There is a course that all students are taking.
(5) Every student is taking at least one course.
(6) There is a course that no students are taking.
(7) Some students are taking no courses.
(8) No course is being taking by all students.
(9) Some courses are being taken by no students.
(10) No student is taking any course.

(a) ∃x ∀y (x, y)
(b) ∃y ∀x (x, y)
(c) ∀x ∃y (x, y)
(d) ¬∃x∃y(x, y)
(e) ∃x∀y C(x, y)
(f) ∀y∃x C(x, y)
(g)∃y∀x -C(x, y)
(h)-∀x∃y C(x, y)
(i) -ay∀xC(x, y)
(j) ∀x∃y-C(x, y)
(k) ∀x∃y-C(х. yy)