## Introduction

We have already studied that a relation is in first normal form (1NF) when every attribute has atomic values. A relation is in second normal form (2NF) when there is no partial dependency in the relation. Similarly, the table is in the third normal form (3NF) when there is no transitive dependency in the relation. We also studied that for a table to be in Boyce Codd Normal form (BCNF), for each FD X->Y, X should be a super key.

Most of the redundancies are reduced after the BCNF. However, there can still be some redundancy even after the table is in BCNF. To solve this problem, we have one more normal form known as the Fourth Normal Form (4NF). This article will discuss the fourth normal form. Before we discuss the fourth normal form, it is important to understand the meaning of multivalued dependency.

Check this out, __DBMS__

## Multivalued dependency

We represent multivalued dependency as X->->Y. It means that for a single value of X, multiple values of Y exist. Consider the following students' relation. The attributes are stud_id, dept_no, and the course.

From the above table, it can be observed that for a given student (stud_id), there can be more than one course in which the student is enrolled. For every student, there is only one department. We can say that:

1. Stud_id -> dept_no: Each student determines the department in which he/she has taken admission.

2. Stud_id ->-> course: Each student "multi determines" the course. This means that one student can enroll in more than one course.

Formally, multivalued dependency represents a dependency between attributes (say X, Y, and Z) in a relation R, such that for each value of X, there is a set of values of Y and Z. However, Y and Z are independent of each other.

A table must have at least three columns in order to have a multivalued dependency.

Now that we know what multivalued dependencies are, we can see how this can lead to redundancy in the relation and how the fourth normal form can be used to remove this redundancy.