To identify the valid primary key for the relation "students," we need to determine a combination of fields that uniquely identify each record in the table.
Given the table:
| student_id | student_name | address | dept_name |
|------------|--------------|---------|-----------|
| 10001 | ROHAN | PUNJAB | BENGALI |
| 10002 | KARTIKA | BIHAR | PHYSICS |
| 10003 | ANINDITA | MUMBAI | HISTORY |
| 10004 | ROHAN | PUNJAB | CHEMISTRY |
| 10001 | PANKAJ | ASSAM | CHEMISTRY |
| 10004 | SUHANA | KERALA | GEOGRAPHY |
We will evaluate each option to see if it can serve as a unique identifier for each row in the table:
a) student_id:
We see that "student_id" 10001 and 10004 are repeated, showing that this cannot uniquely identify each row. Thus, "student_id" alone is not a valid primary key.
b) student name:
Students with the same name ("ROHAN") appear more than once but in different departments. This indicates that "student name" alone does not uniquely identify each row.
c) student name, address:
There are no duplicate "student name" and "address" combinations in the table, but this combination alone is not a common practice to use because different students may have the same name and address. This ambiguity is not suitable for a robust primary key.
d) student_id, dept_name:
When we combine "student_id" and "dept_name," we get the following pairs:
- (10001, BENGALI)
- (10002, PHYSICS)
- (10003, HISTORY)
- (10004, CHEMISTRY)
- (10001, CHEMISTRY)
- (10004, GEOGRAPHY)
No combination of "student_id" and "dept_name" is repeated. Therefore, this combination uniquely identifies each record in the table.
Thus, the valid primary key for the relation "students" is:
[tex]\[
\boxed{\text{student_id, dept_name}}
\][/tex]
