# DBMS/U4 Topic 7 Multivalued Dependencies and forth normal Form

### Rules for 4th Normal Form

For a table to satisfy the Fourth Normal Form, it should satisfy the following two conditions:

- It should be in the
**Boyce-Codd Normal Form**. - And, the table should not have any
**Multi-valued Dependency**.

Let’s try to understand what multi-valued dependency is in the next section.

### What is Multi-valued Dependency?

A table is said to have multi-valued dependency, if the following conditions are true,

- For a dependency A → B, if for a single value of A, multiple value of B exists, then the table may have multi-valued dependency.
- Also, a table should have at-least 3 columns for it to have a multi-valued dependency.
- And, for a relation R(A,B,C), if there is a multi-valued dependency between, A and B, then B and C should be independent of each other.

If all these conditions are true for any relation(table), it is said to have multi-valued dependency.

## Time for an Example

Below we have a college enrolment table with columns s_id, course and hobby.

s_id |
course |
hobby |

1 | Science | Cricket |

1 | Maths | Hockey |

2 | C# | Cricket |

2 | Php | Hockey |

As you can see in the table above, student with s_id **1** has opted for two courses, **Science** and **Maths**, and has two hobbies, **Cricket** and **Hockey**.

You must be thinking what problem this can lead to, right?

Well the two records for student with s_id **1**, will give rise to two more records, as shown below, because for one student, two hobbies exists, hence along with both the courses, these hobbies should be specified.

s_id |
course |
hobby |

1 | Science | Cricket |

1 | Maths | Hockey |

1 | Science | Hockey |

1 | Maths | Cricket |

And, in the table above, there is no relationship between the columns course and hobby. They are independent of each other.

So there is multi-value dependency, which leads to un-necessary repetition of data and other anomalies as well.

### How to satisfy 4th Normal Form?

To make the above relation satify the 4th normal form, we can decompose the table into 2 tables.

**CourseOpted Table**

s_id |
course |

1 | Science |

1 | Maths |

2 | C# |

2 | Php |

And, **Hobbies Table**,

s_id |
hobby |

1 | Cricket |

1 | Hockey |

2 | Cricket |

2 | Hockey |

Now this relation satisfies the fourth normal form.

A table can also have functional dependency along with multi-valued dependency. In that case, the functionally dependent columns are moved in a separate table and the multi-valued dependent columns are moved to separate tables

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