Database Normalization: Understanding Functional Dependencies and Normal Forms, Lecture notes of Database Management Systems (DBMS)

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Normalization

Functional Dependencies

If in a table column X uniquely identifies column Y of

same table then we can say that attribute Y is functionally

dependent of attribute X.

It can represented as X→Y

Types of Functional Dependencies

1. Trivial functional dependency
2. non-trivial functional dependency
3. Multivalued dependency
4. Transitive dependency

Non-trivial Functional Dependency

Multivalued Dependency

Normalization

• Organizing the data in database so that data redundancy, insertion anomaly, update anomaly & deletion anomaly can be avoided is called normalization.
• If a database is not normalized there will be three type of anomalies which occurs: 1. Insertion anomaly 2. Update anomaly 3. Deletion anomaly
• Example-

Example 1-

• Let R(A,B,C,D,E) be a relation with set of functional dependencies {A →B,B →C,D →E}.
• Now we will find the candidate key that is (A,E).
• The table is in 1st^ NF because it has all atomic values but to be in 2nd^ NF all non-prime attribute should have full dependency on key not on the part of key. Here attribute B and C are only dependent on A and E is only dependent on D. so the relation is not in second NF.

Example 2-

• Let R(A,B,C,D,E) be a relation with set of functional dependencies {A →B,B →CD,D →E}.
• Now we will find the candidate key that is A.
• The table is in 1st^ NF because it has all atomic values but to be in 2nd^ NF all non-prime attribute should have full dependency on key not on the part of key. Here all attribute are fully dependent on A. so the relation is in second NF. But there is transitive dependency between A to D and A to E. So the relation is not in 3 NF.