$2\mathrm{.}3$ Modifications to course$\_$offers table

Whenever a course is removed from the course$\_$of fers table, it should also update the st udent$\_$courses table such that all the student entries for that course $($in that particular session and semester$)$ should be removed. The tot$\_$credits in the student table for the removed students should also be updated. If the course is added, ensure that course$\_$id is present in the courses table and professor$\_$id is present in the professor table.

Given an entry that is to be inserted into the course$\_$of fers table, create a trigger that makes sure that a professor does not teach more than $4$ courses in a session. Also make sure that the course is being offered before the associated professor resigns. If in any case the entry is not valid show an "invalid" message or else insert the entry into the table.

$2\mathrm{.}4$ Modifications to department table

Write a single trigger using which on update on the department table, if dept$\_$id is updated, updates all course ids of the courses belonging to that department according to the new dept$\_$id in course$\_$offers, courses and student$\_$courses tables $($i$.$e update the first three digits of the course$\_$id according to new dept$\_$id$),$ also update it in professor and student tables. On delete, before deletion, check if there are no students in the department, if there are students show a "Department has students" message, else delete the department record and further delete all courses from course$\_$offers, courses tables and professors in that department from professor table.