*Relationships Among Normal Forms*

On June 24, 2013, In The Relational Data Model by Admin

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As we have pointed out, 4NF implies BCNF, which in turn implies 3NF. Therefore, the sets of relation schemas (including dependencies) satisfying the three normal forms are related as in the following figure (a). That is, if a relation with certain dependencies is in 4NF, it is also in BCNF and 3NF. Also, if a relation with certain dependencies is in BCNF, then it is in 3NF.

One more way to contrast the normal forms is by the guarantees they make about the set of relations that result from a decomposition into that normal form. These observations are summarized in the table of the following figure (b). That is, BCNF (and therefore 4NF) eliminates the redundancy and other anomalies that are caused by FD's, while only 4NF eliminates the additional redundancy that is caused by the presence of nontrivial MVD's that are not FD's. Sometimes, 3NF is sufficient to eliminate this redundancy, but there are examples where it is not. A decomposition into 3NF can always be chosen so that the FD's are preserved; that is, they are enforced in the decomposed relations (although we have not discussed the algorithm to do so in this blog). BCNF does not guarantee preservation of FD's, and none of the normal forms guarantee preservation of MVD's, though in usual cases the dependencies are preserved.

### Tags

- algorithm
- dependencies
- relations
- schema
- Natural Joins / Theta-Joins
- Selection / Cartesian Product
- Set Operations on Relations
- Relational Algebra
- Document Type Definitions
- XML and Its Data Model
- References
- What If There Is No Key
- Representing ODL Relationships
- Representing Other Type Constructors
- Decomposition into Fourth Normal Form
- Fourth Normal Form
- Third Normal Form
- Recovering Information from a Decomposition
- Decomposition into BCNF
- Projecting Functional Dependencies
- Why the Closure Algorithm Works
- Computing the Closure of Attributes
- Rules About Functional Dependencies
- An Object-Oriented Approach
- Handling Weak Entity Sets
- From E/R Relationships to Relations
- From Entity Sets to Relations
- Equivalent Representations of a Relation
- The Entity-Relationship Data Model