Chapter 2: Relational Model
Information Technology Department
Bryar Hassan (MSc Eng.)
[email protected]
Structure of Relational Database
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A relational database consists of a collection of tables
Relation: it is used to refer to a table in relational model
Tuple: it is used to refer to a row
Attribute: it is used to a column of a table
Relation Instance: it refers to a specific instance of a relation. e.g.,
containing a specific set of rows
Database System Concepts
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Example of Relation
Database System Concepts
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Attribute Types
• The set of allowed values for each attribute is called the domain of
the attribute
• Attribute values are (normally) required to be atomic; that is,
indivisible
• The special value null is a member of every domain
• The null value causes complications in the definition of many
operations
Database System Concepts
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Keys
• We must have a way to specify how tuples within a given relation
are distinguished.
• This is expressed in terms of their attributes.
– The values of the attribute values of a tuple must be such that they can
uniquely identify the tuple.
– No two tuples in a relation are allowed to have exactly the same
value for all attributes.
• A key (whether primary, candidate, or super) is a property of the
entire relation, rather than of the individual tuples
• Super key: is a set of one or more attributes that, taken collectively,
allow us to identify uniquely a tuple in the relation.
• Candidate key: If K is a superkey, then so is any superset of K. We
are often interested in superkeys for which no proper subset is a
superkey. Such minimal superkeys are called candidate keys
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Keys
• Primary key: is a candidate key that is chosen by the database
designer as the principal means of identifying tuples within a
relation
• Foreign key: A relation, say r1, may include among its attributes
the primary key of another relation, say r2. This attribute is called a
foreign key from r1, referencing r2.
– The relation r1 is also called the referencing relation of the foreign key
dependency, and r2 is called the referenced relation of the foreign key
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Primary Key Versus Foreign Key
• A table can only have one primary key. A primary key is a field or
set of fields that:
– Has a unique value for each record
– Is indexed
– Identifies the record
• You can add the primary key from one table to another table to
create a relationship between them. In the other table, it is called a
foreign key.
Database System Concepts
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Primary Key Versus Foreign Key
• A foreign key, simply stated, is another table's primary key. The
values in a foreign key field match values in the primary key,
indicating that the two records are related
• For example, a customer and an order that she has placed. Unlike
primary keys:
– A table can have more than one foreign key.
– A foreign key does not necessarily have unique values.
– A foreign key cannot reliably identify a particular record. For example, you
cannot always tell which record you are viewing from the Orders table by
looking at the Customer ID.
Database System Concepts
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Example
• Suppose you use the primary key of the Customers table in the
Orders table. In the Orders table it is a foreign key.
1. Primary key
2. Foreign key
Database System Concepts
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Database Schema
• Database schema: it is the logical design of the database
• Example of the schema diagram for University database
Database System Concepts
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Relational Algebra
• The relational algebra defines a set of operations on relations,
paralleling the usual algebraic operations such as addition,
subtraction or multiplication, which operate on numbers.
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Just as algebraic operations on numbers take one or more numbers as input and
return a number as output, the relational algebra operations typically take one or
two relations as input and return a relation as output.
Database System Concepts
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Selection of Tuples
Database System Concepts
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Selection of Columns (Attributes)
Database System Concepts
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Joining Two Relations – Cartesian Product
Database System Concepts
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Union of Two Relations
Database System Concepts
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Set Different of Two Relations
Database System Concepts
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Set Intersection of Two Relations
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Joining Two Relations – Natural Join
• Let r and s be relations on schemas R and S
respectively.
Then, the “natural join” of relations R and S is a relation
on schema R  S obtained as follows:
– Consider each pair of tuples tr from r and ts from s.
– If tr and ts have the same value on each of the
attributes in R  S, add a tuple t to the result, where
• t has the same value as tr on r
• t has the same value as ts on s
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Natural Join Example
Database System Concepts
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Summary of Relational Algebra
Database System Concepts
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Summary
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Structure of Relational Database
Attribute Types
Keys
Primary Key Versus Foreign Key
Database Schema
Relational Aljebra
Database System Concepts
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