1. ## Quantifiers

Let C(x,y) mean that x is enrolled in y, where the universe of discourse for x is the set of all students in your school and the universe of discourse for y is the set of all classes being given at your school. Express each of the following statements by a simple English sentence.

(upside down E)x (upside down E)y (upside down A)z ((x does not equal y) ^ (C(x,z)->C(y,z)))

and

(upside down E)x (upside down E)y (upside down A)z ((x does not equal y) ^ (C(x,z)<->C(y,z)))

2. $\left( {\exists x} \right)\left( {\exists y} \right)\left( {\forall z} \right)\left\{ {\left( {x \ne y} \right)\left[ {C(x,z) \to C(y,z)} \right]} \right\}$ could be translated as “There are two students, A & B, such that if A is in any class the B is also in the same class”.
Note that saying two students means A is not B.

BTW: It is known in the trade as backwards E not up-side-down.
The old joke is: “How does one translate $\forall \forall \exists \exists\$”?
Answer: For every up-side-down A there is a backwards E.

3. So, x does not equal y means that there are two students? That is the part I was confused about. Thank you for your help.