Database Modeling and Design

6.1 Fundamentals of Normalization 109
interdependencies among individual attributes associated with those
tables and taking projections (subsets of columns) of larger tables to
form smaller ones.
Let us first review the basic normal forms, which have been well
established in the relational database literature and in practice.
6.1.1 First Normal Form
Definition. A table is in first normal form (1NF) if and only if all columns
contain only atomic values, that is, each column can have
only one value for each row in the table.
Relational database tables, such as the Sales table illustrated in Figure
6.1, have only atomic values for each row and for each column. Such
tables are considered to be in first normal form, the most basic level of
normalized tables.
To better understand the definition for 1NF, it helps to know the difference
between a domain, an attribute, and a column. A domain is the
set of all possible values for a particular type of attribute, but may be
used for more than one attribute. For example, the domain of people’s
names is the underlying set of all possible names that could be used for
either customer-name or salesperson-name in the database table in Figure
6.1. Each column in a relational table represents a single attribute,
but in some cases more than one column may refer to different
attributes from the same domain. When this occurs, the table is still in
1NF because the values in the table are still atomic. In fact, standard SQL
assumes only atomic values and a relational table is by default in 1NF. A
nice explanation of this is given in Muller [1999].
6.1.2 Superkeys, Candidate Keys, and Primary Keys
A table in 1NF often suffers from data duplication, update performance,
and update integrity problems, as noted above. To understand these
issues better, however, we must define the concept of a key in the context
of normalized tables. A superkey is a set of one or more attributes,
which, when taken collectively, allows us to identify uniquely an entity
or table. Any subset of the attributes of a superkey that is also a superkey,
and not reducible to another superkey, is called a candidate key. A primary
key is selected arbitrarily from the set of candidate keys to be used in an
index for that table.