Consider the UNIVERSITY database with the following relations:

STUDENT $($rollNo$,$ name, degree, year, sex, deptNo, advisor$)$

DEPARTMENT $($deptId$,$ name, hod, phone$)$

PROFESSOR $($empId$,$ name, sex, startYear, deptNo, phone$)$

COURSE $($courseId$,$ cname, credits, deptNo$)$

ENROLLMENT $($rollNo$,$ courseId, sem, year, grade$)$

TEACHING $($empId$,$ courseId, sem, year, classRoom$)$

PREREQUISITE$($preReqCourse$,$ courseID$)$

Write relational algebra expressions for the following queries:

i$.$ For each department, find its name and the name, sex and phone number of the department.

ii$.$ Find courses offered by each department.

iii. Find those students who have registered for all courses offered in the de Computer Science.

iv$.$ Obtain the department Ids for departments with no lady professor.

v$.$ Obtain the rollNo of girl students who have obtained at least one $S$ grad