Explain different normal forms (1NF, 2NF, 3NF, BCNF).

Normalization is a database design technique aimed at reducing data redundancy and improving data integrity. There are several normal forms that define different levels of normalization. Let's explore them in detail:

1. First Normal Form (1NF):
The first step in normalizing a database is to ensure it's in first normal form. A table is in 1NF if it satisfies the following conditions:

• Each column of the table must contain atomic (indivisible) values.
• Each column in a row must contain the same type of values.
• Each column must have a unique name.
• The order in which data is stored does not matter.

2. Second Normal Form (2NF):
A table is in 2NF if it is in 1NF and all the non-key columns are fully functionally dependent on the table’s primary key. This means that if the table's primary key is composed of multiple columns, no non-key column should depend only on part of the key but on the entire key.

3. Third Normal Form (3NF):
A table is in 3NF if it is in 2NF and there are no transitive dependencies. This means that if a non-key column depends on another non-key column, it should be moved to a separate table. In other words, every non-key column must provide a fact about the key, the whole key, and nothing but the key.

4. Boyce-Codd Normal Form (BCNF):
BCNF is a more stringent version of 3NF. A table is in BCNF if it is in 3NF and for every one of its non-trivial functional dependencies X -> Y, X is a superkey—that is, X is either a candidate key or a superset thereof. BCNF is designed to eliminate the possibility of anomalies that can still arise in 3NF tables due to certain types of functional dependencies.

What are the key differences between 1NF and 2NF?

The key differences between 1NF and 2NF lie in the nature of the dependencies within the table.

• 1NF focuses on the structure of the data, ensuring that each cell contains atomic values and that the order of data does not matter. It does not address the relationships between data items.
• 2NF, on the other hand, builds on 1NF by eliminating partial dependencies. A partial dependency occurs when a non-key column depends on only part of the primary key in a table with a composite (multi-column) primary key. In 2NF, every non-key column must be fully functionally dependent on the entire primary key.

To illustrate, consider a table in 1NF with a composite primary key. If a non-key column depends only on part of the primary key, it violates 2NF. For example, if a table tracking orders has a composite primary key (OrderID, ProductID) and a column for ProductPrice that depends only on ProductID, moving the ProductPrice to a separate table (with ProductID as the primary key) would bring the original table into 2NF.

How does 3NF help in reducing data redundancy?

Third Normal Form (3NF) plays a crucial role in reducing data redundancy by eliminating transitive dependencies. A transitive dependency occurs when a non-key column depends on another non-key column, which in turn depends on the primary key.

For instance, consider a table in 2NF that includes columns for EmployeeID (primary key), DepartmentID, and DepartmentName. If DepartmentName depends on DepartmentID, which in turn depends on EmployeeID, then DepartmentName has a transitive dependency on EmployeeID through DepartmentID. This setup can lead to data redundancy because the same DepartmentName may be repeated multiple times in the table.

To address this, 3NF would require moving DepartmentName to a separate Department table (with DepartmentID as the primary key), eliminating the transitive dependency. This normalization step ensures that DepartmentName is stored only once, reducing redundancy and improving data integrity. When an update is needed, it must be made in only one place, minimizing the risk of inconsistencies.

Can you provide an example of when BCNF is preferred over 3NF?

Boyce-Codd Normal Form (BCNF) is preferred over Third Normal Form (3NF) when there are functional dependencies where the determinant (left side of the dependency) is not a superkey. BCNF provides a stricter criterion for eliminating anomalies that can persist in 3NF tables.

Consider an example involving a university course registration system:

Table: CourseRegistration

• Columns: StudentID, CourseID, InstructorID

• Functional Dependencies:

  • (StudentID, CourseID) -> InstructorID (primary key)
  • InstructorID -> CourseID (an instructor teaches only one course)

In this scenario, the table is in 3NF because there are no transitive dependencies. However, it violates BCNF because InstructorID -> CourseID means that InstructorID, which is not a superkey, determines another non-key column, CourseID.

To satisfy BCNF, we would need to split the table into two:

Table1: CourseRegistration

• Columns: StudentID, CourseID, InstructorID
• Primary Key: (StudentID, CourseID)

Table2: InstructorCourse

• Columns: InstructorID, CourseID
• Primary Key: InstructorID

By doing this, we ensure that every determinant in the functional dependencies is a superkey, thus meeting the BCNF criteria. This separation eliminates potential anomalies such as insertion, deletion, and update anomalies that could occur if the table remained in 3NF.

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