So the exam was tricky but I feel some questions could be looked at from another way. To start of, in Question 25 which asks about whether Departments cannot exist without sections. The ER diagram can be looked at from the course side of the diagram. The department does not necessarily have to provide a course and if a course may not be offered, there will be no section. I know the answer key says that the analysis is unaffected by the fact that deparments do not have to have courses and I do not understand how.
Now in the Hail Big Sugar Dog ER model, the cardinality is ambiguous. In question 15, if you look at the relationship between offered and course, the cardinality from course to offered is ambiguous. It may have a 0 or 1 minimum requirement. Hence I would argue that the question could be true or false. Similarly for some questions based on this ER diagram, I feel the answers could be argued.