This set of tables is not in 3NF. The primary violation occurs in the Orders table. Specifically, the CustomerID in the Orders table is a non-key attribute that is functionally dependent on the primary key (OrderID). Since CustomerID is not part of the primary key, and it's not fully functionally dependent on the entire primary key (OrderID), this violates 3NF.

Furthermore, the Orders table also contains a non-key attribute, TotalAmount, which is functionally dependent on the combination of OrderID and Quantity and UnitPrice from the OrderItems table. This is another violation of 3NF. The OrderItems table contains a non-key attribute, ProductName, which is functionally dependent on the ProductID in the Products table. This is a violation of 3NF as well.

To achieve 3NF, the tables should be normalized as follows:

• Customers (CustomerID, CustomerName, CustomerEmail, City) - Remains in 3NF
• Orders (OrderID, CustomerID, OrderDate) - TotalAmount should be calculated from OrderItems.
• OrderItems (OrderItemID, OrderID, ProductID, Quantity, UnitPrice) - Remains in 3NF
• Products (ProductID, ProductName, Description, Price) - Remains in 3NF

A possible solution would be to create a new table, OrderTotals, to store the TotalAmount for each order:

This eliminates the redundancy and ensures that the TotalAmount is calculated from the OrderItems table, which is the correct approach.

This set of tables is in 3NF. Let's examine each table:

Students (StudentID, StudentName, CourseID): The primary key is StudentID. StudentName is functionally dependent on StudentID, and CourseID is functionally dependent on StudentID. Therefore, this table is in 3NF.

Courses (CourseID, CourseName, Instructor): The primary key is CourseID. CourseName and Instructor are both functionally dependent on CourseID. Therefore, this table is in 3NF.

Enrollments (EnrollmentID, StudentID, CourseID, Grade): The primary key is EnrollmentID. StudentID and CourseID are both functionally dependent on EnrollmentID. Therefore, this table is in 3NF.

There are no non-key attributes that are not fully functionally dependent on the primary key in any of the tables. Therefore, the entire schema is in 3NF.

Answer:

Normal Form (NF) is a series of rules used to organize a database to reduce data redundancy and improve data integrity. Each normal form builds upon the previous one, addressing specific types of data anomalies.

1NF (First Normal Form): A table is in 1NF if it meets the following criteria:

• Each cell contains only a single value (atomic values).
• There are no repeating groups of columns.

Anomaly Prevented: Repeating groups can lead to inconsistencies when performing operations like insertion, deletion, or updating. For example, if a customer can have multiple phone numbers stored in the same column, updating a phone number for a specific customer becomes difficult.

2NF (Second Normal Form): A table is in 2NF if it is in 1NF and all non-key attributes are fully functionally dependent on the entire primary key. This means no partial dependencies exist.

Anomaly Prevented: Partial dependencies occur when a non-key attribute depends only on a portion of the primary key. For example, in a table with a composite key (e.g., (OrderID, ProductID)), if a non-key attribute depends only on OrderID, it's a partial dependency. This can lead to incorrect updates if only the OrderID is changed.

3NF (Third Normal Form): A table is in 3NF if it is in 2NF and there are no transitive dependencies. This means no non-key attribute depends on another non-key attribute.

Anomaly Prevented: Transitive dependencies occur when a non-key attribute depends on another non-key attribute, which in turn depends on the primary key. For example, if City depends on State and State depends on ZipCode (and ZipCode is part of the primary key), then City has a transitive dependency on the primary key. This can lead to inconsistencies if the State is updated incorrectly.