I am beginner to Advanced Math. I have a assignment that:

Q. 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 of these statements by a simple sentence.
I have a statement:

. . . . .[tex]\exists x\, \exists y\, \forall z\, \bigg((x\, \neq\, y)\, \wedge\, \big(C(x,\, z)\, \rightarrow\, C(y,\, z)\big)\bigg)[/tex]

And the answer is written in that book:

A. There exist at least two students such that if one is enrolled in every courses, then the other
However, I think it should be:

B. There exist at least two different students such that every courses which the one enrolled, then the other.
Are that two sentences, A and B, different? Which sentence is true? Please explain for me.

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