Explanation:

To understand why third normal form (3NF) is inadequate in certain situations, it's important to first understand what 3NF is and what it aims to achieve.

What is Third Normal Form (3NF)?

Third normal form (3NF) is a database normalization technique that aims to eliminate data redundancy and improve data integrity. In 3NF, every non-key attribute (i.e., attribute that is not part of any candidate key) must be functionally dependent on the primary key.

For example, consider a relation called STUDENT with attributes STUD_ID, NAME, AGE, ADDRESS, and COURSE. The primary key is STUD_ID, and the functional dependencies are:

- STUD_ID -> NAME, AGE, ADDRESS
- COURSE -> NAME

To bring this relation to 3NF, we need to split it into two relations:

- STUDENT1 with attributes STUD_ID, NAME, AGE, and ADDRESS
- STUDENT2 with attributes COURSE and NAME

In this way, we eliminate the data redundancy caused by the COURSE -> NAME dependency.

However, there are situations where 3NF is not enough to achieve data integrity. These situations include:

a) Has multiple candidate keys

A candidate key is a set of attributes that can uniquely identify a tuple in a relation. A relation can have multiple candidate keys, and in such cases, 3NF may not be enough to ensure data integrity.

For example, consider a relation called EMPLOYEE with attributes EMP_ID, NAME, AGE, and SALARY. The primary key is EMP_ID, but there is also a candidate key made up of NAME and AGE. In this case, 3NF would not be enough to ensure data integrity because NAME and AGE are not functionally dependent on each other or on EMP_ID.

To bring this relation to a higher normal form, we need to split it into two relations:

- EMPLOYEE1 with attributes EMP_ID, NAME, and AGE
- EMPLOYEE2 with attributes EMP_ID and SALARY

In this way, we eliminate the data redundancy caused by the NAME and AGE candidate key.

b) Has candidate keys that are composite

A composite key is a candidate key made up of two or more attributes. In such cases, 3NF may not be enough to ensure data integrity because the attributes in the composite key may not be functionally dependent on each other.

For example, consider a relation called STUDENT_COURSE with attributes STUD_ID, COURSE_ID, and GRADE. The primary key is (STUD_ID, COURSE_ID), which means that this is a composite key. In this case, 3NF would not be enough to ensure data integrity because GRADE is not functionally dependent on either STUD_ID or COURSE_ID individually.

To bring this relation to a higher normal form, we need to split it into three relations:

- STUDENT with attributes STUD_ID and NAME
- COURSE with attributes COURSE_ID and COURSE_NAME
- GRADE with attributes STUD_ID, COURSE_ID, and GRADE_VALUE

In this way, we eliminate the data redundancy caused by the composite key.

c) Has overlapped candidate keys

An overlapped candidate key is a candidate key that shares one or more attributes with another candidate key. In such cases, 3NF may not be enough to ensure data integrity because the shared attributes may not be functionally dependent on each other.

For example, consider a relation called CUSTOM