Question $1.(50$ marks$)$

Design an ER diagram for a university's academic system:

The university is composed of several departments, each with a unique code, a unique name, and a location.

Each department is led by one head, who is also a professor, and we record from which year the head starts lead the department. A professor can lead at most one department.

Each professor works for a specific department and has a unique employee ID$,$ name, rank, and salary.

A professor can lead a maximum of one research group but can participate in no or multiple groups.

Each research group has a unique group name, a primary focus, a lead researcher who is also a professor, and can have no or multiple other professors participating in it$.$

Each research group hosts a series of events. The details of each event, including the date, topic, and one or multiple invited speakers, are recorded. Events organized by different research groups can occur on the same day or with same topic, but each research group only hosts one event on a given day.

$($a$)$ Draw the ER diagram and state any assumptions you make. Ensure not to introduce extra entities, attributes, or relationships beyond the description provided. $(30$ marks$)$

$($b$)$ For your ER diagram given above, convert it into relational schema using the mapping guidelines discussed in the lecture. For each relation $($table$)$ obtained, specify the name and its attributes, its primary key, as well as foreign key references. $(20$ marks$)$