$(1-6)[15$ points$]$

A university database system is designed to keep track of students, professors, and courses. The system should capture the relationships between these entities, with a particular focus on course enrollment and teaching assignments. Draw an EER diagram for each of the following scenarios, taking into account any additional constraints mentioned.

$(3$ points$)$ Students can enroll in multiple courses, and their enrollment history needs to be recorded, including the semester and year of enrollment for each course.

$(3$ points$)$ Professors can teach multiple courses, but for this database, only the courses currently being taught by each professor are recorded.

$(2$ points$)$ Each student must be enrolled in at least three courses every semester.

$(2$ points$)$ Each professor must teach exactly one course each semester $($no more, no less$).$

$(2$ points$)$ Every course must have at least one student enrolled, and every student must be enrolled in at least one course.

$(3$ points$)$ Modify the model to accommodate the scenario where a course can be co$-$taught by a team of professors. In this case, introduce any necessary entity sets and relationship sets. Assume that for each course, only the professors currently teaching it are recorded.