Intro to DBMS

Fourth Normal Form (4NF)

According to the fourth normal form (4NF), A relation will be in 4NF if,

 It is in BCNF form and has no multi-valued dependency.

Multivalued Dependency

  • For a single value of A, More than one value (either similar or not) of B exists.
  • Multivalued dependency must contain at least 3 attributes (i.e., A, B, C) Because, In the Multivalued dependency, two attributes (i.e., B, C) in a table are independent of each other, but both attributes (B, C) depend on a third attribute (i.e., A)

Notation of Multi-Valued Dependency

Example: Consider the Student Table as given below.

The above table does not hold the conditions of 4NF because it Holds the Multivalued Dependency.


  • FOR std_id =1, there are two values of Std_course (i.e., CS and English), and the same for Std_id =2, there are two values of Std_course (i.e., Java and C#). 
  • Columns “Std_course” and “Std_hobby” are independent of each other but depend on “Std_id”. At least three values also exist in the given table. 

Both points show that Multivalued Dependency exists in the table. As we know, if multivalued dependency exists, then that table is not in 4NF.

How To Satisfy 4th Normal Form?

To remove the 4NF problem and satisfy the 4NF, we can decompose the “Student” table as given below.

Table 01 “Student_Course” 

Table 02 “Student_Hobbies”

As we see, the table is also in 4NF, and for each value of column “A,” more than one value of column “B” exists. Now, this relation satisfies the 4NF.

Functional Dependency And Multi-Valued Dependency

A table can also have functional dependency (FD) along with multi-valued dependency, as given below.

These problems can easily be resolved by table decomposition.