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It does not have any non-prime attribute that is functionally dependent on any proper subset of any candidate key of the relation (i.e. it lacks partial dependencies). A non-prime attribute of a relation is an attribute that is not a part of any candidate key of the relation. Put simply, a relation (or table) is in 2NF if:
The columns in a candidate key are called prime attributes, [3] and a column that does not occur in any candidate key is called a non-prime attribute. Every relation without NULL values will have at least one candidate key: Since there cannot be duplicate rows, the set of all columns is a superkey, and if that is not minimal, some subset of ...
No non-prime attribute of R is transitively dependent on the primary key. A non-prime attribute of R is an attribute that does not belong to any candidate key of R. [3] A transitive dependency is a functional dependency in which X → Z (X determines Z) indirectly, by virtue of X → Y and Y → Z (where it is not the case that Y → X). [4]
Every non-prime attribute has a full functional dependency on each candidate key (attributes depend on the whole of every key) [5] Every non-trivial functional dependency either begins with a superkey or ends with a prime attribute (attributes depend only on candidate keys) [5]
B → C direct dependency relationship exists. Then the functional dependency A → C is a transitive dependency (which follows the axiom of transitivity ). In database normalization , one of the important features of third normal form is that it excludes certain types of transitive dependencies.
Because all three attributes are prime attributes (i.e. belong to candidate keys), the table is in 3NF. The table is not in BCNF, however, as the Shop type attribute is functionally dependent on a non-superkey: Nearest shop. The violation of BCNF means that the table is subject to anomalies.
Normalization (to first normal form) is a process where attributes with non-simple domains are extracted to separate stand-alone relations. The extracted relations are amended with foreign keys referring to the primary key of the relation which contained it. The process can be applied recursively to non-simple domains nested in multiple levels. [4]
APL uses the term operator in Heaviside’s sense as a moderator of a function as opposed to some other programming language's use of the same term as something that operates on data, ref. relational operator and operators generally.