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

\(\pi_{salary}(\sigma_{name='Gold'}(instructor))\)

\(|\sigma_{salary>80000}(instructor)|\)

\(\pi_{building}(\sigma_{dept\_name='Music'}(department))\)

\(|instructor \bowtie_{instructor.dept\_name=department.dept\_name} department|\)

\(\pi_{name}(\sigma_{budget=50000}(instructor \bowtie_{instructor.dept\_name=department.dept\_name} department))\)

\(|\pi_{building}(department)|\)

\(\pi_{dept\_name}(\sigma_{salary=72000}(instructor))\)

\(|\pi_{salary}(instructor)|\)

\(\pi_{name}(instructor) - \pi_{name}(\sigma_{salary>42000}(instructor))\)

\(|\sigma_{budget<80000}(department)|\)

\(\pi_{ID}(\sigma_{salary=72000}(instructor))\)

\(|\sigma_{salary<budget}(instructor \bowtie_{instructor.dept\_name=department.dept\_name} department)|\)

\(\pi_{dept\_name}(instructor) \cap \pi_{dept\_name}(\sigma_{building='Watson'}(department))\)

\(|\sigma_{salary=40000}(instructor)|\)

\(\pi_{budget}(\sigma_{dept\_name='Comp. Sci.'}(department))\)

\(|\pi_{dept\_name}(instructor) - \pi_{dept\_name}(department)|\)

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

\(\pi_{building}(\sigma_{salary=95000}(instructor \bowtie_{instructor.dept\_name=department.dept\_name} department))\)

\(|\pi_{name}(instructor) - \pi_{name}(\sigma_{dept\_name='Finance'}(instructor))|\)