Third Normal Form

Third normal form (3NF) is based on the concept of transitivedependency.
A functional dependency X?Y in a relation schema R is a
transitive dependency if there exists a set of attributes Z in R that is neither a candidate key nor a subset of any key of R, and both X?Z and Z?Y hold.

Definition. According to Codd’s original definition, a relation schema R is in 3NF if it satisfies 2NF and no nonprime attribute of R is transitively dependent on the primary key.

General Definitions of Second and Third Normal Forms
In general, we want to design our relation schemas so that they have neither partial nor transitive dependencies because these types of dependencies cause the update anomalies seen previously.
The steps for normalization into 3NF relations that we have discussed so far disallow partial and transitive dependencies on the primary key. The normalization procedure described so far is useful for analysis in practical situations for a given database where primary keys have already been defined.
Summary of Normal Forms Based on Primary Keys and
Corresponding Normalization

Normal Form Test Remedy (Normalization)
First (1NF) Relation should have no
multivalued attributes or nested
relations Form new relations for each
multivalued attribute or nested
relation.
Second (2NF) For relations where primary key
contains multiple attributes, no nonkey attribute should be functionally dependent on a part of the primary key. Decompose and set up a new
relation for each partial key with its dependent attribute(s). Make sure to keep a relation with the original primary key and any attributes that are fully functionally dependent on it.
Third (3NF) Relation should not have a nonkey attribute functionally determined by another nonkey attribute (or by a set of nonkey attributes). That is, there should be no transitive dependency of a nonkey attribute on the primary key Decompose and setup a relation that includes the nonkey attribute(s) that functionally determine(s) other nonkey attribute(s).

As a general definition of prime attribute, an attribute that is part of any candidate key will be considered as prime. Partial and full functional dependencies and transitive dependencies will now be considered with respect to all candidate keys of a relation.
Prime attributes are part of any candidate key Non-prime attribute are not.


General Definition of Second Normal Form
A relation schema R is in second normal form (2NF) if every nonprime attribute A in R is not partially dependent on any key of R.
The test for 2NF involves testing for functional dependencies whose left-hand side attributes are part of the primary key. If the primary key contains a single attribute, the test need not be applied at all.