$2.$ A university registrar$$s office maintains data about the following entities:

$($a$)$ courses, including number, title, credits, syllabus, and prerequisites. A course may have more than one prerequisite.

$($b$)$ course offerings, including course number, year, semester, section number, instructor$($s$),$ timings, and classroom. There may be more than one section for a course in a semester.

$($c$)$ students, including student$-$id$,$ name, and program.

$($d$)$ instructors, including identification number, name, department, and title. An instructor may teach more than one course in a semester.

$($e$)$ the enrollment of students in courses and grades awarded to students in each course they are enrolled for must be appropriately modeled.

i$.$ Construct an ERD for the registrar$$s office. Document all assumptions that you make about mapping constraints. Identify the key of each entity. Each relationship should show its cardinality. $(15$ marks$)$

ii$.$ Map the designed ERD into a relation model. The relations should show their primary keys, and the foreign keys should connect to their corresponding primary keys. $(10$ marks$)$