\(\pi_{dept\_name}(instructor) - \pi_{dept\_name}(student)\)

\(\pi_{instructor.dept\_name}(instructor \bowtie_{instructor.dept\_name=student.dept\_name} student)\)

\(\pi_{dept\_name}(student) - \pi_{dept\_name}(instructor)\)

\(\pi_{dept\_name}(department)\)

\(\pi_{dept\_name}(instructor) \cap \pi_{dept\_name}(student)\)

\(\pi_{name}(instructor)\)

\(\pi_{name}(\sigma_{salary>90000}(instructor))\)

\(\pi_{instructor.name}(\sigma_{department.budget>90000}(instructor \bowtie_{instructor.dept\_name=department.dept\_name} department))\)

\(\pi_{name}(instructor \bowtie_{instructor.salary=department.budget} department)\)

\(\pi_{name}(\sigma_{budget>90000}(department))\)

\(\pi_{name}(\sigma_{dept\_name='Taylor'}(student))\)

\(\pi_{student.name}(\sigma_{department.building='Taylor'}(student \bowtie_{student.dept\_name=department.dept\_name} department))\)

\(\pi_{name}(student)\)

\(\pi_{name}(department)\)

\(\pi_{name}(student \bowtie_{student.ID=department.budget} department)\)

\(\pi_{instructor.dept\_name}(instructor \bowtie_{instructor.dept\_name=student.dept\_name} student)\)

\(\pi_{dept\_name}(department)\)

\(\pi_{dept\_name}(department) - \pi_{dept\_name}(student)\)

\(\pi_{dept\_name}(instructor) \cap \pi_{dept\_name}(student)\)

\(\pi_{dept\_name}(student) - \pi_{dept\_name}(instructor)\)

\(\pi_{name}(student)\)

\(\pi_{instructor.name}(\sigma_{department.building='Watson'}(instructor \bowtie_{instructor.dept\_name=department.dept\_name} department)) \cup \pi_{student.name}(\sigma_{department.building='Watson'}(student \bowtie_{student.dept\_name=department.dept\_name} department))\)

\(\pi_{name}(instructor)\)

\(\pi_{student.name}(student \bowtie_{student.ID=instructor.ID} instructor)\)

\(\pi_{name}(department)\)

\(\pi_{instructor.name}(instructor \bowtie_{instructor.dept\_name=student.dept\_name} student)\)

\(\pi_{name}(student)\)

\(\pi_{name}(department)\)

\(\pi_{name}(instructor) - \pi_{instructor.name}(instructor \bowtie_{instructor.dept\_name=student.dept\_name} student)\)

\(\pi_{name}(instructor)\)

\(\pi_{name}(student) - \pi_{name}(instructor)\)

\(\pi_{name}(department)\)

\(\pi_{name}(instructor) \cup \pi_{name}(student)\)

\(\pi_{instructor.name}(instructor \bowtie_{instructor.name=student.name} student)\)

\(\pi_{name}(instructor) \cap \pi_{name}(student)\)

\(\pi_{dept\_name}(\sigma_{budget<70000}(department))\)

\(\pi_{name}(\sigma_{dept\_name='Physics'}(instructor))\)

\(\pi_{name}(student)\)

\(\pi_{name}(instructor)\)

\(\pi_{instructor.name}(\sigma_{department.budget<70000}(instructor \bowtie_{instructor.dept\_name=department.dept\_name} department))\)

\(\pi_{student.name}(student \bowtie_{student.ID=instructor.ID} instructor)\)

\(\pi_{student.name}(\sigma_{salary>90000}(instructor))\)

\(\pi_{student.name}(\sigma_{instructor.salary>90000}(student \bowtie_{student.dept\_name=instructor.dept\_name} instructor))\)

\(\pi_{student.name}(\sigma_{student.tot\_cred>90000}(student))\)

\(\pi_{student.name}(student)\)

\(\pi_{dept\_name}(instructor)\)

\(\pi_{dept\_name}(department)\)

\(\pi_{department.dept\_name}(\sigma_{instructor.salary>department.budget}(instructor \bowtie_{instructor.dept\_name=department.dept\_name} department))\)

\(\pi_{dept\_name}(\sigma_{salary>budget}(department))\)

\(\pi_{dept\_name}(student)\)