Explain the concept of multi-valued dependency in database normalization.

In database normalization, a multi-valued dependency refers to a situation where a relationship between two sets of attributes exists, and for every value in one set, there can be multiple corresponding values in the other set. This means that the values in one set are not dependent on each other, but rather on the values in the other set.

To better understand this concept, let's consider an example. Suppose we have a database table called "Employees" with the following attributes: EmployeeID, EmployeeName, and Skills. In this case, the EmployeeID uniquely identifies each employee, and the EmployeeName represents the name of the employee. However, the Skills attribute can have multiple values for each employee, as an employee can possess multiple skills.

Now, let's say we have the following data in the Employees table:

EmployeeID | EmployeeName | Skills
----------------------------------
1 | John | Programming, Database Management
2 | Jane | Programming, Project Management
3 | Mark | Database Management

In this example, we can observe that the Skills attribute has multiple values separated by commas. This indicates a multi-valued dependency between the EmployeeID and Skills attributes. The values in the Skills attribute are not dependent on each other but rather on the EmployeeID.

To normalize this table and remove the multi-valued dependency, we can create a separate table called "EmployeeSkills" with the attributes EmployeeID and Skill. This new table will have a one-to-many relationship with the Employees table, where each employee can have multiple skills.

The normalized tables would look like this:

Employees table:
EmployeeID | EmployeeName
-------------------------
1 | John
2 | Jane
3 | Mark

EmployeeSkills table:
EmployeeID | Skill
-----------------
1 | Programming
1 | Database Management
2 | Programming
2 | Project Management
3 | Database Management

By separating the multi-valued attribute into a separate table, we eliminate redundancy and ensure data integrity. This is the essence of database normalization, which aims to organize data in a structured and efficient manner.