Consider the following library management system. The library contains a large collection of books, magazines, and DVDs$.$ Each item $($book$,$ magazine, DVD$)$ has a unique ID$,$ title, publication date, and genre. The library serves many members who are identified by member ID$,$ and have a name, address, and phone number.

Members can borrow multiple items. Each borrowing record should include a unique transaction ID$,$ the date of borrowing, and the date of return. Books and DVDs can be borrowed for a period of up to $3$ weeks, while magazines can be borrowed for $1$ week.

Furthermore, the library employs several staff members, each having a staff ID$,$ name, position, and salary. Staff members are responsible for managing the borrowing process and maintaining the library$$s inventory.

Finally, the library organizes events such as book readings or educational workshops, where each event has a unique event ID$,$ name, date, and associated staff member who organizes it$.$

$.$

a$.[5$ marks$]$ Draw the conceptual schema $($i$.$e$.,$ the ER diagram$)$ for this application.

b$.[5$ marks$]$ Show all the functional dependencies that should hold among the attributes.

c$.[3$ marks$]$ Draw the relational schemas for the database that are each in Third Normal Form $(3$NF$)$