Normal Forms

In database theory, normal forms are a series of guidelines used to standardize the structure of relational database schemas to minimize redundancy and avoid anomalies in data operations. The most important normal forms range from the first to the fifth normal form (1NF to 5NF) and the Boyce-Codd Normal Form (BCNF). Here is an overview:

1. First Normal Form (1NF):

   • Definition: A relation schema is in 1NF if all attribute values are atomic, meaning each attribute contains only indivisible values.
   • Goal: Eliminate repeating groups and ensure that the data is in tabular form.

2. Second Normal Form (2NF):

   • Definition: A relation schema is in 2NF if it is in 1NF and every non-key attribute is fully functionally dependent on the entire primary key.
   • Goal: Eliminate partial dependencies, where a non-key attribute depends on part of a composite primary key.
3. Third Normal Form (3NF):
   • Definition: A relation schema is in 3NF if it is in 2NF and no non-key attribute is transitively dependent on the primary key.
   • Goal: Eliminate transitive dependencies to ensure non-key attributes depend only on the primary key.
4. Boyce-Codd Normal Form (BCNF):
   • Definition: A relation schema is in BCNF if it is in 3NF and every non-trivial functional dependency $X\to Y$ (where $Y$ is not a subset of $X$) implies that $X$ is a superkey.
   • Goal: A stricter form of 3NF to avoid all dependency anomalies.
5. Fourth Normal Form (4NF):
   • Definition: A relation schema is in 4NF if it is in BCNF and has no non-trivial multi-valued dependencies.
   • Goal: Eliminate multi-valued dependencies where an attribute depends on another attribute and also has multiple independent values.
6. Fifth Normal Form (5NF):

• • Definition: A relation schema is in 5NF if it is in 4NF and every join dependency in the schema is implied by the candidate keys.
  • Goal: Eliminate join dependencies to ensure relations can be decomposed and recombined without information loss.

These normal forms aim to optimize data structures, minimize redundancy, and ensure data integrity. While not all normal forms are applied in practice to the highest level, they provide a theoretical foundation for designing robust and efficient databases.