Now you should write statements (as the ones above) in Z-Notation for the following sets or predicates. Do not give the set as answer (e.g. {Hans, Klaus, Jule} for all students taking 315) but specify in Z-Notation how this set can be created. Even when the systems state changes and more students take 315 the set you get with your specification should always give you all students that take the course (e.g. {s : Student | c : Course | c.name = 315 (a, c) Takes}). Specify a

1. set including all courses that are taken by at least student. With the given state of the system all courses but 515 should be included, since the others are all taken by at least one student.

2. set including all students that take at least one course

3. predicate that evaluates to true if all students take a course - answer the following: Would this would evaluate to true in our given system state?

4. set including all students that do not take a course. Answer which students would be included in this set.

5. predicate that evaluates to true if a specific student X takes exactly 2 courses (X is the name of the student we are looking for, X could then be substituted with any of the students names in the system and tell us if the student takes exactly 2 courses) - answer the following: For which students would this evaluate to true?

6. predicate that evaluates to true if a course with the name X (X is the course name this time) is taken by all students - answer the following : Would this evaluate to true in our given system state?

Task 1: Sets (36 points) Look at the following Class diagram, which is an object view of a current system state. The objects on the left are of type Student and the objects on the right of type Course. Takes Hans 215 Takes Takes Karl 315 Takes Andrea S15 Klaus 415 Jule Takes Task 1: Sets (36 points) Look at the following Class diagram, which is an object view of a current system state. The objects on the left are of type Student and the objects on the right of type Course. Takes Hans 215 Takes Takes Karl 315 Takes Andrea S15 Klaus 415 Jule Takes