: Chapter – 2 :

Relational Data

Model

Introduction Relational data model allows various data

packets/files to be related to each other with a set of relations.

For example, if customer names are stored in one file ‘CUSTOMER’, and other file contains the names of cities ‘CITY’. Then CUSTOMER file can have a relation with CITY, which will help identify which city the customer belongs to. 

The data is arranged in a relation which is visually represented in a two dimensional table.

The data is inserted into the table in the form of tuples (which are nothing but rows).

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A tuple is formed by one or more than one attributes, which are used as basic building blocks in the formation of various expressions that are used to derive a meaningful information.

There can be any number of tuples in the table, but all the tuple contain fixed and same attributes with varying values. 

The relational model is implemented in database where a relation is represented by a table, a tuple is represented by a row, an attribute is represented by a column of the table, attribute name is the name of the column.

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All the relational algebra operations, such as Select, Intersection, Product, Union, Difference, Project, Join, Division, Merge etc. can also be performed on the Relational Database Model.

Operations on the Relational Database Model are facilitated with the help of different conditional expressions, various key attributes, pre-defined constraints etc.

Keys….. Candidate Key :-

Any field or a combination of fields that identifies a record uniquely is called a Candidate Key. The Candidate Key cannot contain NULL value and should always contain a unique value.

Primary Key :-Primary key is nothing but a candidate key that identifies a record uniquely.

Foreign Key :-A Foreign key is a primary key for other table, in which it uniquely identifies a record. A Foreign Key defines relation between two (or more) tables. A Foreign key can contain NULL value.

Super Key :-Given Relation Schema R with U is the list of attributes, there are a set which is a subset of U. If in a relation r of K with any two distinct tuples t1 and t2 we have the constraints that t1[K] ≠ t2[K] then K is called a SUPER KEY of relation schema R.

A SUPER KEY is defined in the relational model as a set of attributes of a relation variable (relvar) for which it holds that in all relations assigned to that variable there are no two distinct tuples (rows) that have the same values for the attributes in this set. Equivalently a super key can also be defined as a set of attributes of a relvar upon which all attributes of the relvar are functionally dependent.

Candidate Key :-

A Super Key can have a redundant attribute. A super key that have no such attributes is called a CANDIDTE KEY.

We can define a Candidate Key as follow : Given relation schema R K’ is the candidate key of R if K’ is satisfied two constraints :

K’ is a super Key of R. There is no such a proper subset of K’ that is

also a super key of R or K’ is a minimal super key.

Since a relational schema can have more then one Candidate Key thus there is a chosen candidate key whose values are used to identify tuple in the relation. Such a key is PRIMARY KEY. Primary key is usually a most common candidate key.

Example :-State Code SrNo RegNo Chassis No VehicleGJ3AB 9999 G1235RF452 1254GG54F HONDA CITYHR4BC 7 HR1546TT32 3256SDF45 HONDA CIVICMH4FF 1000 MH45HGJ215 458HYU789 HONDA CITYGJ3BM 6045 GJ11HAS2125 653ASD458 PLATINA

Super Key :- {StateCode, SrNo, RegNo}, {RegNo}, {RegNo, ChassisNo}

Candidate Key :- {StateCode, SrNo}, {RegNo}Primary Key :-{StateCode, SrNo}, {RegNo}

Fundamental Concepts in Relational Model

Domain :-  A domain D is the original sets of atomic values

used to model data.

By atomic, we mean that each value in the domain is indivisible as far as the relational model is concerned. For example:

• The domain of day shift is the set of all possible days : {Mon, Tue, Wed…}

• The domain of salary is the set of all floating-point numbers greater than 0 and less than 200,000 (say).

• The domain of name is the set of character strings that represents names of person

Relation :-

A relation is a subset of the Cartesian product of a list of domains characterized by a name. Relation can be viewed as a “table”. In that table, each row represents a tuple of data values and each column represents an attribute.

Attribute :-

A column of a relation designated by name. The name associated should be meaningful. Each attributes associates with a domain.

Relation Schema :-

Denoted by R is a list of attributes (A1, A2, …, An) The degree of the relation is the number of

attributes of its relation schema. The cardinality of the relation is the number of

tuples in the relation.

Characteristics of Relations

Ordering of Tuples in relation :-A tuple is a set of values. A relation is a set of tuples. Since a relation is a set, there is no ordering on rows.

Ordering of Values with a tuple :-The order of attributes and their values within a relation is not important as long as the correspondence between attributes and values is maintained.

Values and NULL Values in the tuple :-Each value in a tuple is atomic. That means each value cannot be divided into smaller components. Hence, the composite and multivalued attributes are not allowed in a relation.

Constraints in Relational Data

Relational model support a well-defined theory of constraint on attributes or tables.

Constraint is useful because it allows designer to specify the semantics of data in database and it is the rules to enforce DBMS to check that new data satisfies the semantics.

Domain restrict the values of attributes in the relation and it is a constraint of relational model.

We need more specific way to state what data values are/are not allows, what format is suitable for an attributes. For example, employee number must be unique, employees’ age is in the range [23, 65].

Such information is provided in logical statements called integrity constraints.

There are several kinds of integrity constraints: Key Constraints. Referential Constraints.

Key Constraints :-A relation is a set of tuples. By definition, all elements in a set are distinct hence all tuple in a relation must be distinct.In relational model, tuples have no identity like object –identification. Tuple identity is totally value-based.Therefore, we need key constraint that is the way of uniquely identify a tuple.

There are many key constraints are there Like : Super Key. Primary Key. Candidate Key. Not Null. Unique Key etc…

Referential Constraints :-The constraint that is specified between two relations and maintain the correspondence between tuples in these relations. It means the reference from a tuple in one relation to other relation must be valid. Referential constraint in relational model relates to notation of foreign key.

Foreign Key Constraints :-A Set of attributes FK in a relational schema R1 is foreign key if :

The attributes in FK correspond to the attributes in the primary key of another relation schema R2.

The value for FK in each tuple of R1 either occur as values of primary key of a tuple in R2 or is entirely NULL

In a database of many relations, there are usually many foreign keys. They provide the “glue” that links individual relations into a cohesive database structure.

Entity-Relationship Model

Entity-Relationship (E-R) data model was developed to facilitate database design by allowing specification of an enterprise schema that represent the overall logical structure of a database.

The E-R model is very useful in mapping the meanings and interaction of real-world enterprises into a conceptual schema.

E-R data model employs three basic notations: Entity Sets Relationship Sets Attributes

1. Entity Sets :-

What is Entity ?

An Entity is a “Thing” or “Object” in real-world that is distinguishable from all other objects.e.g. Each person in an enterprise is an entity.

Entity has a set of properties and the values for some set of properties may uniquely identify an entity.e.g. A person have a “personID” property and its value “101-A45” would uniquely identify that particular entity.

What is Entity Sets?

An Entity Set is the set of entities of the same type that share some properties or attributes.e.g. Set of all persons who are customer at a given bank can be define as the entity set customer.Similarly entity set loan might represent the set of all loans awarded by particular bank.

Entity Set do not need to be Disjoint.e.g. It can be possible that entity set of all employees of the bank and entity set of all customer of the bank, so a person entity may be employ or customer or both or neither of these.

An entity is represented by a set of attributes.

The attributes are Descriptive Properties processed by each member of an entity set.

Designation of an attribute for an entity set expresses that the database stores similar information concerning each entity.

e.g. Possible attributes for entity set customer :

custNo, custName, custAdd, custCity….etc…

Thus database includes a collection of entity sets, each of which contains any number of entities of the same types.

• A database usually contains groups of entities that are similar. For example, a company employing

• hundreds of employees may want to store similar information concerning each of the employees. These

• employee entities share the same attributes, but each entity has its own value(s) for each attribute.

• An entity type defines a collection (or set) of entities that have the same attributes.

• A few individual entities of each type are also illustrated, along with the values of their attributes.

• The collection of all entities of a particular entity type in the database at any point in time is called an entity set; the entity set is usually referred to using the same name as the entity type.

• For example :-

• EMPLOYEE refers to both a type of entity as well as the current set of all employee entities in the database.

• An entity type describes the schema or intension for a set of entities that share the same structure.

• The collection of entities of a particular entity type are grouped into an entity set, which is also called the

• extension of the entity type.

2. Relationship Sets :-

What is Relationship?

A relationship is an association among several entities.e.g. We can define relationship that assciated “Customer Hays Loan”.

What is Relationship Set?

A relationship Set is a set of relationship of the same type.

It is mathematical relation on n > 2 entity sets.

If E1, E2……, En are entity set then the relationship ser R is the subset of:{(e1,e2…en)|e1 є E1, e2 є E2, …., en є En} e.g. Entity sets Loan and entity set Branch which define the relationship set Loan_Branch which denote the association between Loan and Branch in which the loan is maintain.

A function that entity plays in relationship is called “Entity’s Role”.

Some entity sets participate in relationship set more then once in different role called “Recursive Relationship Set”.

e.g. Consider a entity set “employee” that records the information about all the employees of bank we may have a relationship “work for” that is modeled by ordered pairs of “employee”.So first employee pair work as Worker and second employ pair work as Manager.

A relationship may also have attributes called “Descriptive Attributes”.

e.g. Relationship Depositor with entity set Customer and Account we can associate the attribute Access_Date to relationship to specify the most recent date a Customer access an Account.

Descriptive Attribute (Access_Date)

Descriptive Attribute

3. Attributes :-

For each attribute, there is a set of permitted values called the Domain or value set of that attribute.

The domain of attribute cust_name might be a set of all text string of a certain length.

An attribute, as used in E-R Model, can be characterize by the following attribute types:

1. Simple and Composite Attributes.2. Single-Value and Multivalued Attributes.3. Derived Attributes.

3.1. Simple and Composite Attributes :- Attributes those used in our examples are of

simple attributes, they have not been divided into a subpart.

Composite attribute on the other hand can be divided into a subpart.

For example : An attribute name could be structured as a composite attribute consisting of Surname, Name, F_Name.

Name

Surname Name F_Name

Address

CityStreet_Add

State Zip

Street_Nm App_NoStreet_No

Attributes that are not divisible are called Simple or Atomic Attributes.

If a composite referenced only as a whole there is no need to subdivide it into component attributes.

For example if there is no need to refer to an individual components of an address then the whole address can be designated as a simple attribute.

3.2. Single-Value and Multivalued Attributes :-

Most attributes nave a single value for any particular entity; such attributes are called Single-Valued Attributes.

For example Age is a single-valued attribute of a person.

In some cases an attribute can have a set of values for the same entity – for example, a color attribute for a car or a college degree attribute for a person.

Cars with one color have a single value whereas two tones cars have a two colors value.

Similarly one person may not have a college degree, another person may have one college degree and third person may have two or more college degree; therefore different person may have different number of values for the same attribute.

Such attributes are called Multivalued attributes.

3.3. Stored and Derived Attributes :-

In some cases two or more attribute values are related – for example Age and Birth_date attributes of a person.

For a particular person entity the value of Age can be determined from the current date and the value of the person’s a Birth_Date. The Age attribute hence called Derived Attribute and is said to be Derivable Attribute from Birth_Date attribute which is called Stored Attribute.

Multivalued Attributes are shown in E-R diagram using this symbol

3.4. Null Value Attributes :- In some cases particular entity may not have

an applicable value for an attribute. For example Apartment_No attribute of an

address applies only to address that are in apartment building not to other type of residency. Similarly a College_Degree attribute applies only to person with college degree.

For such situation a special value called NULL is created.

A single family home would have a NULL value for Apartment_No and a person with no college degree would have a NULL value for College_degree.

In two cases the value of an attribute would have the NULL. Known Unknown

Attribute value is exist but missing that is Known. E.g. :- Height of a Person

Attribute value when it not sure whether it is exist or not that is Unknown. E.g. :- Home Phone.

3.5. Complex Attributes :- Composite and Multivalued Attributes can be nested

arbitrarily. We can represent nesting by grouping components

of a composite attributes between Parentheses ( ) and separating a component with comma (,) and by displaying Multivalued attributes by Braces { }.

Such an attributes are called Complex Attributes. For example a person can have more then one

residencies and each residency can have one address and multiple phones then :Address ( Sreet_add ( S_Num,S_Name,App_No), City,

State, Zip, Phone { Add_Phone (Code,Ph_No),

Mobile })

4. Alternative E_R Notations :-

Entity Weak Entity

Relationship Identifying Relationship

Attribute Multivalued Attribute

Key Attribute Derived Attribute

Composite Attribute