John has a high IQ.
All students are members of the university. All graduate students are students. All PhD students are graduate students. Some PhD students have high IQs. If John is not a PhD student, then he is not a member of the university. If John has a high IQ, then he is a PhD student or a graduate student.
∀x (Student(x) → MemberOfUniversity(x)) ∀x (GraduateStudent(x) → Student(x)) ∀x (PhDStudent(x) → GraduateStudent(x)) ∃x (PhDStudent(x) ∧ HighIQ(x)) ¬PhDStudent(john) → ¬MemberOfUniversity(john) HighIQ(john) → PhDStudent(john) ⊕ GraduateStudent(john)