# Multivalued Dependency

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## Overview

**Multivalued dependency (MVD)** states that two independent data variable rows say **'B'** and **'C'** in a table can be dependent on the third variable row **'A'** respectively, i.e., for same value of attribute **'A'**, we can have multiple values of component **'B'** and **'C'**.

## 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,**

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

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

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

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

**R1[a]**,**R2[a]**,**R3[a]**,**R4[a]**should contain the same value.- 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.

Row | Name | Course_work | Hobby |
---|---|---|---|

R1 | Rahul | C++ | Painting |

R2 | Rahul | Python | Music |

R3 | Rahul | C++ | Music |

R4 | Rahul | Python | Painting |

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**

Finding from the table,

Therefore, condition 1 seems to be satisfied.

**Condition 2 for MVD**

Finding from the table,

Therefore, condition 2 also seems to be satisfied.

Now coming to the last condition which is

**Condition 3 for MVD**

Finding from the table, we can conclude

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

So theoretically, we have

And from the table, we got

And for,

We have

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

## Conclusion

**Multivalued Dependency** exists when the values two independent attributes, say **b** and **c**, are determined based on the third attribute **a**.

MVD is represented as **'a --> --> b'**.

Therefore, we can say that for a **multivalued dependency** to exist in a relation R.

- Two components say
**B**and**C**of a single attribute say**A**should be mutually independent of eachother. - For two tuples of R, say
**A**and**B**, for entire attributes of**A**, component**B**might have different values. - Similarly, For two tuples of R, say
**A**and**C**, for entire attributes of**A**the component**C**might have different values.