Problem 1 is really simple but 2 is confusing me a little. I'm going on the assumption that $x$ and $y$ are both students and they are saying $z$ is the class? Is it really as simple as what I wrote or am I missing something?
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.
1) C(Randy Goldberg, CS 252)
2) $\exists x\exists y\forall z((x\neq y) \land (C(x, z)\to C(y, z)))$
1) The student Randy Goldberg is enrolled in the class CS252.
2) All classes have multiple students.
Or should 2 be: Each class has two different students enrolled in it.
Best Answer
Statement 2 means that, there is some distinct pair of students $x,y$ such that for any class $z$ if student $x$ is enrolled in class $z$ then student $y$ is enrolled in class $z$.
Edit: I read the quantifiers backwards. Fixed.