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, f) ∃x∃y∀z((x ≠ y) ∧ (c(x, z) ↔ c(y,

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.