Please consider the following case study for ER modeling.

The University Course Management System is designed to track information about students, professors, courses, and course registrations. It consists of several entities that store information about Students, Professors, Courses, Departments, and Scholarships. The Student entity has attributes Student$\_$ID $($a unique identifier$),$ Student$\_$Name, and Major. The Professor entity has attributes Professor$\_$ID $($a unique identifier$),$ Professor$\_$Name, and Department$\_$ID$.$ The Course entity has attributes Course$\_$ID $($a unique identifier$),$ Course$\_$Name, and Description. The Department entity has attributes Department$\_$ID $($a unique identifier$),$ Department$\_$Name, and Department$\_$Head. The Scholarship entity has attributes Scholarship$\_$ID $($a unique identifier$)$ and Amount.

As for the relationships among these entities, a Student can enroll in multiple Courses, and a Course can have multiple Students. The registration information for a student in a course, which is identified by the IDs of the student and the course together, also includes the grade and date of enrollment. A Department has multiple Professors, and a Professor belongs to one Department. A Student has one Advisor, and an Advisor $($who is a Professor$)$ can advise multiple Students. Each Student is awarded one Scholarship, and each Scholarship is awarded to one Student. There are two types of Students in the university: Undergraduate and Graduate. These two types of students are exclusive of each other, and there are only these two types of students in the university. Both types of students have common attributes such as student ID$,$ name, and major, but they also have unique attributes such as GPA for Undergraduates and Research Area for Graduates.

Please note that in this case study, the names of people such as students, professors, and department heads are not unique $($i$.$e$.,$ the people with the same name may correspond to different IDs$).$ Additionally, due to the re$-$coding of courses and departments in history, the same course information $($including the course name and description$)$ and department name may correspond to different course IDs and department IDs, respectively.

In this context, answer the following questions:

$($a$)$ How do we classify binary relationships into $1-$to$-1$ relationships, $1-$to$-$many relationships and many$-$to$-$many relationships in the ER modeling?

$($b$)$ What is the $``$enhanced$"$ feature for the Enhanced Entity$-$Relationship $($EER$)$ diagrams when compared with the ordinary ER diagrams?

$($c$)$ Draw an Entity$-$Relationship diagram for this database using UML notation, including all the entities mentioned above, together with their attributes $($including primary key attributes$),$ relationships, and multiplicity constraints. Note that generalisation$/$specification will be involved in the ER diagram. Only include the following entities in the ER diagram: Student, Undergraduate, Graduate, Professor, Course, Department, and Scholarship. Please use the UML notation to draw the ER diagram, as taught in the lectures and practicals. Only use the attributes given in the instructions, and do not make up any other attributes yourself or use other names for the attributes.

$($d$)$ Write down the relational schema that results from translating the EER diagram. Please properly highlight the primary key for each of the resulting tables. Please follow the rules we teach in the class for the translation.