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Third Normal Form (3NF) in DBMS

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The Third Normal Form (3NF) is a further step in the normalization process after achieving Second Normal Form (2NF). A relation is considered to be in 3NF if:

1. It is already in 2NF:

• This means the relation has no partial dependencies of non-key attributes on the primary key.

2. No Transitive Dependencies:

• All non-key attributes are functionally dependent only on the primary key and not on any other non-key attributes. If there is a dependency of one non-key attribute on another non-key attribute, it is called a transitive dependency, and such a dependency violates 3NF.

Simply put, in 3NF, non-key attributes should not depend on other non-key attributes; they should only depend on the primary key.

Example for Third Normal Form (3NF)

Consider a table storing information about products sold by different vendors:

| Product_ID | Product_Name | Vendor_Name | Vendor_Address  |
|------------|--------------|-------------|-----------------|
| P1         | Laptop       | TechCorp    | 123 Tech St.    |
| P2         | Mouse        | TechCorp    | 123 Tech St.    |
| P3         | Chair        | FurniShop   | 456 Furni Rd.   |

In the table above, `Product_ID` is the primary key. We can see that `Vendor_Address` depends on `Vendor_Name` rather than `Product_ID`, which represents a transitive dependency.

To convert this table to 3NF, we can split it into two tables:

Product Table

| Product_ID | Product_Name | Vendor_Name |
|------------|--------------|-------------|
| P1         | Laptop       | TechCorp    |
| P2         | Mouse        | TechCorp    |
| P3         | Chair        | FurniShop   |

Vendor Table

| Vendor_Name | Vendor_Address  |
|-------------|-----------------|
| TechCorp    | 123 Tech St.    |
| FurniShop   | 456 Furni Rd.   |

Now, the `Product` table has `Product_ID` as the primary key, and all attributes in this table depend only on the primary key. The `Vendor` table has `Vendor_Name` as its primary key, and the address in this table depends only on the vendor name.

This normalization eliminates the transitive dependency and reduces redundancy. If we need to change a vendor's address, we now only have to make the change in one place in the `Vendor` table.

To further refine the database structure, we might proceed to other normalization forms like BCNF, but 3NF is often sufficient for many practical applications and strikes a good balance between minimizing redundancy and maintaining a manageable schema.

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