Write the following queries in SQL. No duplicates should be printed for any answer.

Consider the following relations: Student(snum: integer, sname: string, major: string, level: string, age: integer)

Class(name: string, time: TIME, room: string, fid: integer)

Enrolled(snum: integer, cname: string)

Faculty(fid: integer, fname: string, deptid: integer)

The meaning of these relations is straightforward; for example, Enrolled has one record per student-class pair such that the student is enrolled in the class.

Find the major in which the most students have more than one class with a given professor.

Find all pairs of students taking the same courses.

Find all pairs of students taking courses from the same professors.

For each major, find the student with the largest gap in their schedule (time between two classes).