Multivalued Dependency

Introduction

So, before we dive into the Multivalued Dependency of DBMS it’s a prerequisite that we should have a proper idea about how Data Base Management System works, for that you can refer to: “Data Base Management System” for better understanding.

Occurrence of Multivalued Dependency(MVD)

• Multivalued Dependency occurs when two attributes in a table are independent of each other but are dependent on the third attribute.
• Since multivalued Dependency consists of a minimum of two variables (independent of each other) to be dependent on the third variable, so the minimum amount of variables required is two.

Representation of Multivalued Dependency(MVD)

we write MVD as,

a --> --> b

Which signifies for a single attribute 'a', there exist multiple values of 'b'.

The above expression is read as: 'a is multi-valued dependent on b'.

Condition For MVD

We can say multivalued dependency exists if all the following conditions are met.

If any attribute 'a' has multiple dependence on 'b', for any relation R, for all the pair data values in row R1 and row R2 in table, such that the relation

R1[a]=R2[a] 

exists, and the relation between row R3 and row R4 exists in table, such that

R1[a] = R2[a] = R3[a] = R4[a]

R1[b] = R3[b], R2[b] = R4[b] 

then we can say that Multivalued Dependency(MVD) exists.

Which means, in the Rows R1, R2, R3, and R4

1. R1[a], R2[a], R3[a], R4[a] should contain the same value.
2. The value of R1[b] should be equal to the value R3[b] and the value R2[b] should be equal to the value of R4[b].

Example of MVD

Now, let's make things clear by taking an example of MVD. Suppose a student named Rahul, who is taking courses on C++ and Python and has hobbies in Painting and Music.

Here Hobby and Course work are multivalued dependents on Name because for the same value of name "Rahul" we have different values of Project and Hobby.

Verification of Example

Now, let us check the condition of MVD on our table,

Condition 1 for MVD

R1[a] = R2[a] = R3[a] = R4[a]

Finding from the table,

R1[a] = R2[a] = R3[a] = R4[a] = 'Rahul'

Therefore, condition 1 seems to be satisfied.

Condition 2 for MVD

R1[b] = R3[b], R2[b] = R4[b] 

Finding from the table,

R1[b] = R3[b] = 'C++', R2[b] = R4[b] = 'Python'

Therefore, condition 2 also seems to be satisfied.

Now coming to the last condition which is

Condition 3 for MVD

R1[c] = R4[c], R2[c] = R3[c] 

Finding from the table, we can conclude

R1[c] = R4[c] = 'Painting', R2[c] = R3[c] = 'Music'

Therefore, condition 3 is also satisfied which means MVD exists in the given example.

So theoretically, we have

a --> --> b 

And from the table, we got

Name --> --> Course work

And for,

a --> --> c

We have

Name --> --> Hobby 

Finally, we can conclude in the given table with conditional relation as

Name --> --> Course Work
Name --> --> Hobby