Joe is not a PhD student.
No students are doctors. All people taking classes are students.  All graduate students are people taking classes.  All PhD students are graduate students.  If Joe is a graduate student or a doctor (but not both), then Joe is not a graduate student and a student.
∀x (Student(x) → ¬Doctor(x)) ∀x (TakingClass(x) → Student(x)) ∀x (GraduateStudent(x) → TakingClass(x)) ∀x (PhDStudent(x) → GraduateStudent(x)) GraduateStudent(joe) ⊕  Doctor(joe) → ¬(GraduateStudent(joe) ^ Student(joe))