# Second normal form

Second normal form (2NF) is a normal form used in database normalization. 2NF was originally defined by E.F. Codd in 1971.[1]

A table that is in first normal form (1NF) must meet additional criteria if it is to qualify for second normal form. Specifically: a table is in 2NF if and only if it is in 1NF and no non-prime attribute is dependent on any proper subset of any candidate key of the table. A non-prime attribute of a table is an attribute that is not a part of any candidate key of the table.

Put simply, a table is in 2NF if and only if it is in 1NF and every non-prime attribute of the table is dependent on the whole of every candidate key.

## Example

Consider a table describing employees' skills:

Employees' Skills
Employee Skill Current Work Location
Brown Light Cleaning 73 Industrial Way
Brown Typing 73 Industrial Way
Harrison Light Cleaning 73 Industrial Way
Jones Shorthand 114 Main Street
Jones Typing 114 Main Street
Jones Whittling 114 Main Street

Neither {Employee} nor {Skill} is a candidate key for the table. This is because a given Employee might need to appear more than once (the employee might have multiple Skills), and a given Skill might need to appear more than once (it might be possessed by multiple Employees). Only the composite key {Employee, Skill} qualifies as a candidate key for the table.

The remaining attribute, Current Work Location, is dependent on only part of the candidate key, namely Employee. Therefore the table is not in 2NF. Note the redundancy in the way Current Work Locations are represented: we are told three times that Jones works at 114 Main Street, and twice that Brown works at 73 Industrial Way. This redundancy makes the table vulnerable to update anomalies: it is, for example, possible to update Jones' work location on his "Shorthand" and "Typing" records and not update his "Whittling" record. The resulting data would imply contradictory answers to the question "What is Jones' current work location?", unless it is meant that Jones exercises different skills at different locations.

A 2NF alternative to this design would represent the same information in two tables: an "Employees" table with candidate key {Employee}, and an "Employees' Skills" table with candidate key {Employee, Skill}:

Employees
Employee Current Work Location
Brown 73 Industrial Way
Harrison 73 Industrial Way
Jones 114 Main Street
Employees' Skills
Employee Skill
Brown Light Cleaning
Brown Typing
Harrison Light Cleaning
Jones Shorthand
Jones Typing
Jones Whittling

Neither of these tables can suffer from update anomalies.

Not all 2NF tables are free from update anomalies, however. An example of a 2NF table which suffers from update anomalies is:

Tournament Winners
Tournament Year Winner Winner Date of Birth
Des Moines Masters 1998 Chip Masterson 14 March 1977
Indiana Invitational 1998 Al Fredrickson 21 July 1975
Cleveland Open 1999 Bob Albertson 28 September 1968
Des Moines Masters 1999 Al Fredrickson 21 July 1975
Indiana Invitational 1999 Chip Masterson 14 March 1977

Even though Winner and Winner Date of Birth are determined by the whole key {Tournament, Year} and not part of it, particular Winner / Winner Date of Birth combinations are shown redundantly on multiple records. This leads to an update anomaly: if updates are not carried out consistently, a particular winner could be shown as having two different dates of birth.

The underlying problem is the transitive dependency to which the Winner Date of Birth attribute is subject. Winner Date of Birth actually depends on Winner, which in turn depends on the key Tournament / Year.

This problem is addressed by third normal form (3NF).

## 2NF and candidate keys

A functional dependency on part of any candidate key is a violation of 2NF. In addition to the primary key, the table may contain other candidate keys; it is necessary to establish that no non-prime attributes have part-key dependencies on any of these candidate keys.

Multiple candidate keys occur in the following table:

Electric Toothbrush Models
Manufacturer Model Model Full Name Manufacturer Country
Forte X-Prime Forte X-Prime Italy
Forte Ultraclean Forte Ultraclean Italy
Dent-o-Fresh EZbrush Dent-o-Fresh EZbrush USA
Kobayashi ST-60 Kobayashi ST-60 Japan
Hoch Toothmaster Hoch Toothmaster Germany
Hoch X-Prime Hoch X-Prime Germany

Even if the designer has specified the primary key as {Model Full Name}, the table is not in 2NF. {Manufacturer, Model} is also a candidate key, and Manufacturer Country is dependent on a proper subset of it: Manufacturer. To make the design conform to 2NF, it is necessary to have two tables:

Electric Toothbrush Manufacturers
Manufacturer Manufacturer Country
Forte Italy
Dent-o-Fresh USA
Kobayashi Japan
Hoch Germany
Electric Toothbrush Models
Manufacturer Model Model Full Name
Forte X-Prime Forte X-Prime
Forte Ultraclean Forte Ultraclean
Dent-o-Fresh EZbrush Dent-o-Fresh EZbrush
Kobayashi ST-60 Kobayashi ST-60
Hoch Toothmaster Hoch Toothmaster
Hoch X-Prime Hoch X-Prime