Let C (x, y) mean that student x is enrolled in class y, where the domain for x consists of all students in your school and the domain for y consists of all classes being given at your school. Express each of these statements by a simple English sentence. a) C (Randy Goldberg, CS 252) b) ∃xC (x, Math 695) c) ∃yC (Carol Sitea, y) d) ∃x (C (x, Math 222) ∧ C (x, CS 252)) e) ∃x∃y∀z ((x ≠ y) ∧ (C (x, z) → C (y, z))) f) ∃x∃y∀z ((x ≠ y) ∧ (C (x, z) ↔ C (y, z)))

a) C (Randy Goldberg, CS 252)

Randy Goldberg is enroled to class CS 252

b) ∃xC (x, Math 695)

There is a student that's enrolled to math clase 695

c) ∃yC (Carol Sitea, y)

There is a class where Carol Sitea is enrolled.

d) ∃x (C (x, Math 222) ∧ C (x, CS 252))

There is a student that's enrolled in math 222 class and in CS 252

e) ∃x∃y∀z ((x ≠ y) ∧ (C (x, z) → C (y, z)))

There are two students (that arn't the same person) that, for every class, if one is enrroled, the other is enrrolled too.

f) ∃x∃y∀z ((x ≠ y) ∧ (C (x, z) ↔ C (y, z)))

There are two students (that arn't the same person) that, for every class, they only are enrolled to the class if the other is enrroled too.