Relations

A relational database contains multiple tables/relations.

A relation is a set of tuples where each attribute is part of a domain.

Relations are represented as tables.

The columns of the table represent attributes of the relation and the rows/tuples represent the relationship between the entities i.e. the values for the relation.

The following is an example of a relation:

More about attributes

• The set of allowed values for an attribute is called the domain of the attribute

• Attribute values are atomic i.e. indivisible (they can't be divided into sub-domains)

• The special value null is a member of every domain; it means that the value is not available or is unknown

• This null value may cause complications in the definition of many operations

• Aggregate functions ignore null values

Relational Schema and Instance

A relational schema consists of a set of attributes and their domains.

$R = (A_1, A_2, ..., A_n)$ where $A_1, A_2, ..., A_n$ are attributes of the relation.

An relation instance refers to the tuples of a relation at a particular point in time. It is denoted as a table.

Note that relations are unordered i.e. the order in which the tuples are present in the table is irrelevant.

Database

A database consists of multiple relations.

For example, a university database can have relations including student, instructor, advisor, department etc.

It is good to have separate relations instead of combining all the attributes into a single table. If we use a single table to represent everything, there would be two main issues:

• redundancy: ex. more than one student having the same instructor

• null values: ex. a student who doesn't have an advisor

The following figure illustrates the university database:

Best practices to design "good" relational schemas will be discussed under normalization theory.