Mysql - Table design for authorization checking

Question

I have a table called Student and it is used to save the relationship between Class and Student

Class	Student (PK)
Class 1	Peter
Class 1	Harry
Class 2	Sally
Class 2	Tommy

And there is another table called Teacher

Teacher(PK)
John
Emma
Chris

Finally, a many to many table is used for authorization and describe the responsibility of each teacher. For example, John can access the profile and Academic performance of every student of Class 1

Teacher (PK)	Class(PK)
John	Class 1
Chris	Class 2
Emma	Class 2

The basic structure is work properly. However, Chris, who should be teacher of class 2 but he needs to access the profile of Peter from Class A because of special reason. Therefore, I try to update the table structure.

Teacher(PK)	Class(PK)	Student
John	Class 1	Null
Chris	Class 1	Peter
Chris	Class 2	Null
Emma	Class 2	Null

Error is thrown because the key "Chris-Class1" is duplicated but I can't set student as part of primary key because nullable is not allow. There are a few methods that can be solved:

1. Add an auto increment field can remove the primary key setting of teacher and class

Index(PK)	Teacher	Class	Student
1	John	Class 1	Null
2	Chris	Class 1	Peter
3	Chris	Class 2	Null
4	Emma	Class 2	Null

2. Or separate it to two tables

Teacher (PK)	Class(PK)
John	Class 1
Chris	Class 2
Emma	Class 2

Teacher(PK)	Class(PK)	Student(PK)
Chris	Class 1	Peter

I would like to ask which approach should be better to handle this case?

Answer 1

he needs to access the profile of Peter from Class A

Use two JOINs rather than adding an extra table.

(Maybe I can be clearer if you provide that 'profile' and provide SHOW CREATE TABLEs.)