Database Table Normalization

Question

Table 1

id  Student
1   Ali
2   Akram
3   Aamir
4   Adeel
5   Aun

Table 2

id  Course
1   English
2   Urdu
3   Maths
4   Physics
5   Chemistry


Table 3

id  stu_id   course_id
1   1          1
2   1          2
3   2          1
4   2          5
5   5          1

Q1: Are these tables normalized ?

Q2: Help me to remove duplicates from table 3, suppose if table 2 have 1000 courses, and student id 1 and 2 are enrolled in all courses, table 3 will be very large because of 2000 entries , is there any way to reduce these ?

Answer 1

1. It is normalized with a many-to-many relation;
2. Yes max cardinality of a many-to-many relation like that is max students x max courses, nothing terrible;
3. In many-to-many relationships use the multiple columns key of the ids couple, you do not need another id;
4. If by duplicates you mean the fact you have many equal fields in the columns, that are not duplicates at all. They mean that a student has many courses and viceversa. What has to be unique is the couple stu_id-course_id.

Regards