What is Functional Dependency?

Functional Dependency (FD) is a constraint that determines the relation of

one attribute to another attribute in a Database Management System (DBMS).
Functional Dependency helps to maintain the quality of data in the database.
It plays a vital role to find the difference between good and bad database
design.
A functional dependency is denoted by an arrow “→”. The functional
dependency of X on Y is represented by X → Y. Let’s understand Functional
Dependency in DBMS with example.
Example:
Employee number Employee Name Salary
1 Dana 50000 San Franci
2 Francis 38000 London
3 Andrew 25000 Tokyo
In this example, if we know the value of Employee number, we can obtain
Employee Name, city, salary, etc. By this, we can say that the city, Employee
Name, and salary are functionally depended on Employee number.
In this tutorial, you will learn:
 Key terms
 Rules of Functional Dependencies
 Types of Functional Dependencies in DBMS
 Multivalued dependency in DBMS
 Trivial Functional dependency in DBMS
 Non trivial Functional dependency in DBMS
 Transitive dependency in DBMS
 What is Normalization?
 Advantages of Functional Dependency

Key terms
Here, are some key terms for Functional Dependency in Database:
Key Terms Description
Axioms is a set of inference rules used to infer all the functional dependen
Axiom
relational database.
It is a rule that suggests if you have a table that appears to contain two en
Decompositio
determined by the same primary key then you should consider breaking th
n
different tables.
Dependent It is displayed on the right side of the functional dependency diagram.
 Key Terms Description
Determinant It is displayed on the left side of the functional dependency Diagram.
It suggests that if two tables are separate, and the PK is the same, you sh
Union
putting them. together

Rules of Functional Dependencies

Below are the Three most important rules for Functional Dependency in
Database:
 Reflexive rule –. If X is a set of attributes and Y is_subset_of X, then X
holds a value of Y.
 Augmentation rule: When x -> y holds, and c is attribute set, then ac ->
bc also holds. That is adding attributes which do not change the basic
dependencies.
 Transitivity rule: This rule is very much similar to the transitive rule in
algebra if x -> y holds and y -> z holds, then x -> z also holds. X -> y is
called as functionally that determines y.

Types of Functional Dependencies in DBMS

There are mainly four types of Functional Dependency in DBMS. Following
are the types of Functional Dependencies in DBMS:
 Multivalued Dependency
 Trivial Functional Dependency
 Non-Trivial Functional Dependency
 Transitive Dependency

Multivalued Dependency in DBMS

Multivalued dependency occurs in the situation where there are multiple
independent multivalued attributes in a single table. A multivalued
dependency is a complete constraint between two sets of attributes in a
relation. It requires that certain tuples be present in a relation. Consider the
following Multivalued Dependency Example to understand.

Example:
Car_model Maf_year C
H001 2017 Metallic
H001 2017 Green
H005 2018 Metallic
H005 2018 Blue
H010 2015 Metallic
 Car_model Maf_year C
H033 2012 Gray
In this example, maf_year and color are independent of each other but
dependent on car_model. In this example, these two columns are said to be
multivalue dependent on car_model.
This dependence can be represented like this:
car_model -> maf_year
car_model-> colour
Trivial Functional Dependency in DBMS
The Trivial dependency is a set of attributes which are called a trivial if the set
of attributes are included in that attribute.
So, X -> Y is a trivial functional dependency if Y is a subset of X. Let’s
understand with a Trivial Functional Dependency Example.
For example:
Emp_id Emp_name
AS555 Harry
AS811 George
AS999 Kevin
Consider this table of with two columns Emp_id and Emp_name.
{Emp_id, Emp_name} -> Emp_id is a trivial functional dependency as Emp_id
is a subset of {Emp_id,Emp_name}.
Non Trivial Functional Dependency in DBMS
Functional dependency which also known as a nontrivial dependency occurs
when A->B holds true where B is not a subset of A. In a relationship, if
attribute B is not a subset of attribute A, then it is considered as a non-trivial
dependency.
Company CEO
Microsoft Satya Nadella 5
Google Sundar Pichai 4
Apple Tim Cook 5
Example:
(Company} -> {CEO} (if we know the Company, we knows the CEO name)
But CEO is not a subset of Company, and hence it’s non-trivial functional
dependency.
Transitive Dependency in DBMS
A Transitive Dependency is a type of functional dependency which happens
when “t” is indirectly formed by two functional dependencies. Let’s understand
with the following Transitive Dependency Example.
Example:
Company CEO
Microsoft Satya Nadella 5
Google Sundar Pichai 4
Alibaba Jack Ma 5
{Company} -> {CEO} (if we know the compay, we know its CEO’s name)
{CEO } -> {Age} If we know the CEO, we know the Age
Therefore according to the rule of rule of transitive dependency:
{ Company} -> {Age} should hold, that makes sense because if we know the
company name, we can know his age.

Advantages/Purpose of Functional Dependency

 Functional Dependency avoids data redundancy. Therefore same data
do not repeat at multiple locations in that database
 It helps you to maintain the quality of data in the database
 It helps you to defined meanings and constraints of databases
 It helps you to identify bad designs
 It helps you to find the facts regarding the database design

Redundancy means having multiple copies of same data in the database. This
problem arises when a database is not normalized. Suppose a table of student
details attributes are: student Id, student name, college name, college rank,
course opted.

As it can be observed that values of attribute college name, college rank,

course is being repeated which can lead to problems. Problems caused due to
redundancy are: Insertion anomaly, Deletion anomaly, and Updation anomaly.

1. Insertion Anomaly –
If a student detail has to be inserted whose course is not being decided yet then
insertion will not be possible till the time course is decided for student.
This problem happens when the insertion of a data record is not possible
without adding some additional unrelated data to the record.

2. Deletion Anomaly –
If the details of students in this table are deleted then the details of college will
also get deleted which should not occur by common sense.
This anomaly happens when deletion of a data record results in losing some
unrelated information that was stored as part of the record that was deleted
from a table.
It is not possible to delete some information without loosing some other
information in the table as well.

3. Updation Anomaly –
Suppose if the rank of the college changes then changes will have to be all over
the database which will be time-consuming and computationally costly.
An update anomaly is a data inconsistency that results from data redundancy
and a partial update. For example, each employee in a company has a
department associated with them as well as the student group they participate
in.

Employee_ID Name Department Student_Group

123 J. Longfellow Accounting Beta Alpha Psi

234 B. Rech Marketing Marketing Club

234 B. Rech Marketing Management Club

456 A. Bruchs CIS Technology Org.

456 A. Bruchs CIS Beta Alpha Psi

If A. Bruch's department is an error it must be updated at least 2 times or there

will be inconsistent data in the database. If the user performing the update does
not realize the data is stored redundantly, the update will not be done properly.

A deletion anomaly is the unintended loss of data due to deletion of other data.
For example, if the student group Beta Alpha Psi disbanded and was deleted
from the table above, J. Longfellow and the Accounting department would cease
to exist. This results in database inconsistencies and is an example of how
combining information that does not really belong together into one table can
cause problems.

An insertion anomaly is the inability to add data to the database due to absence
of other data. For example, assume Student_Group is defined so that null values
are not allowed. If a new employee is hired but not immediately assigned to a
Student_Group then this employee could not be entered into the database. This
results in database inconsistencies due to omission.

Fully-functional dependency in DBMS

DBMSDatabaseMySQL

An attribute is fully functional dependent on another attribute, if it is Functionally

Dependent on that attribute and not on any of its proper subset.
For example, an attribute Q is fully functional dependent on another attribute P, if it is
Functionally Dependent on P and not on any of the proper subset of P.
Let us see an example −
<ProjectCost>
ProjectID ProjectCost

001 1000

001 5000

<EmployeeProject>
EmpID ProjectID Days

E099 001 320

E056 002 190

The above relations states that −

Days are the number of days spent on the project.
EmpID, ProjectID, ProjectCost -> Days
However, it is not fully functional dependent.
Whereas the subset {EmpID, ProjectID} can easily determine the {Days} spent on the
project by the employee.
This summarizes and gives our fully functional dependency −
{EmpID, ProjectID} -> (Days)

Relational Decomposition
o When a relation in the relational model is not in appropriate normal form then the
decomposition of a relation is required.
o In a database, it breaks the table into multiple tables.
o If the relation has no proper decomposition, then it may lead to problems like loss of
information.
o Decomposition is used to eliminate some of the problems of bad design like anomalies,
inconsistencies, and redundancy.

Types of Decomposition

Lossless Decomposition
 o If the information is not lost from the relation that is decomposed, then the
decomposition will be lossless.
o The lossless decomposition guarantees that the join of relations will result in the same
relation as it was decomposed.
o The relation is said to be lossless decomposition if natural joins of all the decomposition
give the original relation.
Example:
EMPLOYEE_DEPARTMENT table:

EMP_ID EMP_NAME EMP_AGE EMP_CITY DEPT_ID DEPT_NAME

22 Denim 28 Mumbai 827 Sales

33 Alina 25 Delhi 438 Marketing

46 Stephan 30 Bangalore 869 Finance

52 Katherine 36 Mumbai 575 Production

60 Jack 40 Noida 678 Testing

The above relation is decomposed into two relations EMPLOYEE and DEPARTMENT
EMPLOYEE table:

EMP_ID EMP_NAME EMP_AGE EMP_CITY

22 Denim 28 Mumbai

33 Alina 25 Delhi

46 Stephan 30 Bangalore

52 Katherine 36 Mumbai
 60 Jack 40 Noida

DEPARTMENT table

DEPT_ID EMP_ID DEPT_NAME

827 22 Sales

438 33 Marketing

869 46 Finance

575 52 Production

678 60 Testing

Now, when these two relations are joined on the common column "EMP_ID", then the
resultant relation will look like:
Employee ⋈ Department

EMP_ID EMP_NAME EMP_AGE EMP_CITY DEPT_ID DEPT_NAME

22 Denim 28 Mumbai 827 Sales

33 Alina 25 Delhi 438 Marketing

46 Stephan 30 Bangalore 869 Finance

52 Katherine 36 Mumbai 575 Production

60 Jack 40 Noida 678 Testing

Hence, the decomposition is Lossless join decomposition.

Dependency Preserving
 o It is an important constraint of the database.
o In the dependency preservation, at least one decomposed table must satisfy every
dependency.
o If a relation R is decomposed into relation R1 and R2, then the dependencies of R either
must be a part of R1 or R2 or must be derivable from the combination of functional
dependencies of R1 and R2.
o For example, suppose there is a relation R (A, B, C, D) with functional dependency set (A-
>BC). The relational R is decomposed into R1(ABC) and R2(AD) which is dependency
preserving because FD A->BC is a part of relation R1(ABC).

Normalization
A large database defined as a single relation may result in data duplication. This
repetition of data may result in:
o Making relations very large.
o It isn't easy to maintain and update data as it would involve searching many records in
relation.
o Wastage and poor utilization of disk space and resources.
o The likelihood of errors and inconsistencies increases.
So to handle these problems, we should analyze and decompose the relations with
redundant data into smaller, simpler, and well-structured relations that are satisfy
desirable properties. Normalization is a process of decomposing the relations into
relations with fewer attributes.

What is Normalization?
o Normalization is the process of organizing the data in the database.
o Normalization is used to minimize the redundancy from a relation or set of relations. It is
also used to eliminate undesirable characteristics like Insertion, Update, and Deletion
Anomalies.
o Normalization divides the larger table into smaller and links them using relationships.
o The normal form is used to reduce redundancy from the database table.
Why do we need Normalization?
The main reason for normalizing the relations is removing these anomalies. Failure to
eliminate anomalies leads to data redundancy and can cause data integrity and other
problems as the database grows. Normalization consists of a series of guidelines that
helps to guide you in creating a good database structure.
Data modification anomalies can be categorized into three types:
o Insertion Anomaly: Insertion Anomaly refers to when one cannot insert a new tuple into
a relationship due to lack of data.
o Deletion Anomaly: The delete anomaly refers to the situation where the deletion of
data results in the unintended loss of some other important data.
o Updatation Anomaly: The update anomaly is when an update of a single data value
requires multiple rows of data to be updated.

Types of Normal Forms:

Normalization works through a series of stages called Normal forms. The normal forms
apply to individual relations. The relation is said to be in particular normal form if it
satisfies constraints.
Following are the various types of Normal forms:

Normal Description
Form

1NF A relation is in 1NF if it contains an atomic value.

2NF A relation will be in 2NF if it is in 1NF and all non-key attributes are fully functional
dependent on the primary key.

3NF A relation will be in 3NF if it is in 2NF and no transition dependency exists.

BCNF A stronger definition of 3NF is known as Boyce Codd's normal form.

4NF A relation will be in 4NF if it is in Boyce Codd's normal form and has no multi-valued
dependency.

5NF A relation is in 5NF. If it is in 4NF and does not contain any join dependency, joining
should be lossless.

Advantages of Normalization
o Normalization helps to minimize data redundancy.
o Greater overall database organization.
o Data consistency within the database.
o Much more flexible database design.
o Enforces the concept of relational integrity.

Disadvantages of Normalization
o You cannot start building the database before knowing what the user needs.
o The performance degrades when normalizing the relations to higher normal forms, i.e.,
4NF, 5NF.
o It is very time-consuming and difficult to normalize relations of a higher degree.
o Careless decomposition may lead to a bad database design, leading to serious problems.

First Normal Form (1NF)

o A relation will be 1NF if it contains an atomic value.
 o It states that an attribute of a table cannot hold multiple values. It must hold only single-
valued attribute.
o First normal form disallows the multi-valued attribute, composite attribute, and their
combinations.
Example: Relation EMPLOYEE is not in 1NF because of multi-valued attribute
EMP_PHONE.
EMPLOYEE table:

EMP_ID EMP_NAME EMP_PHONE EMP_STATE

14 John 7272826385, UP
9064738238

20 Harry 8574783832 Bihar

12 Sam 7390372389, Punjab

8589830302

The decomposition of the EMPLOYEE table into 1NF has been shown below:

EMP_ID EMP_NAME EMP_PHONE EMP_STATE

14 John 7272826385 UP

14 John 9064738238 UP

20 Harry 8574783832 Bihar

12 Sam 7390372389 Punjab

12 Sam 8589830302 Punjab

Second Normal Form (2NF)
o In the 2NF, relational must be in 1NF.
o In the second normal form, all non-key attributes are fully functional dependent on the
primary key
Example: Let's assume, a school can store the data of teachers and the subjects they
teach. In a school, a teacher can teach more than one subject.
TEACHER table

TEACHER_ID SUBJECT TEACHER_AGE

25 Chemistry 30

25 Biology 30

47 English 35

83 Math 38

83 Computer 38

In the given table, non-prime attribute TEACHER_AGE is dependent on TEACHER_ID

which is a proper subset of a candidate key. That's why it violates the rule for 2NF.
To convert the given table into 2NF, we decompose it into two tables:
TEACHER_DETAIL table:

TEACHER_ID TEACHER_AGE

25 30

47 35

83 38

TEACHER_SUBJECT table:
 TEACHER_ID SUBJECT

25 Chemistry

25 Biology

47 English

83 Math

83 Computer

Third Normal Form (3NF)

o A relation will be in 3NF if it is in 2NF and not contain any transitive partial dependency.
o 3NF is used to reduce the data duplication. It is also used to achieve the data integrity.
o If there is no transitive dependency for non-prime attributes, then the relation must be in
third normal form.
A relation is in third normal form if it holds atleast one of the following conditions for
every non-trivial function dependency X → Y.
1. X is a super key.
2. Y is a prime attribute, i.e., each element of Y is part of some candidate key.
Example:
EMPLOYEE_DETAIL table:

EMP_ID EMP_NAME EMP_ZIP EMP_STATE EMP_CITY

222 Harry 201010 UP Noida

333 Stephan 02228 US Boston

 444 Lan 60007 US Chicago

555 Katharine 06389 UK Norwich

666 John 462007 MP Bhopal

Super key in the table above:

1. {EMP_ID}, {EMP_ID, EMP_NAME}, {EMP_ID, EMP_NAME, EMP_ZIP}....so on
Candidate key: {EMP_ID}
Non-prime attributes: In the given table, all attributes except EMP_ID are non-
prime.
Here, EMP_STATE & EMP_CITY dependent on EMP_ZIP and EMP_ZIP dependent
on EMP_ID. The non-prime attributes (EMP_STATE, EMP_CITY) transitively
dependent on super key(EMP_ID). It violates the rule of third normal form.
That's why we need to move the EMP_CITY and EMP_STATE to the new
<EMPLOYEE_ZIP> table, with EMP_ZIP as a Primary key.
EMPLOYEE table:

EMP_ID EMP_NAME EMP_ZIP

222 Harry 201010

333 Stephan 02228

444 Lan 60007

555 Katharine 06389

666 John 462007

EMPLOYEE_ZIP table:

EMP_ZIP EMP_STATE EMP_CITY

 201010 UP Noida

02228 US Boston

60007 US Chicago

06389 UK Norwich

462007 MP Bhopal

Boyce Codd normal form (BCNF)

o BCNF is the advance version of 3NF. It is stricter than 3NF.
o A table is in BCNF if every functional dependency X → Y, X is the super key of the table.
o For BCNF, the table should be in 3NF, and for every FD, LHS is super key.
Example: Let's assume there is a company where employees work in more than one
department.
EMPLOYEE table:

EMP_ID EMP_COUNTRY EMP_DEPT DEPT_TYPE EMP_DEPT_NO

264 India Designing D394 283

264 India Testing D394 300

364 UK Stores D283 232

364 UK Developing D283 549

In the above table Functional dependencies are as follows:

1. EMP_ID → EMP_COUNTRY
2. EMP_DEPT → {DEPT_TYPE, EMP_DEPT_NO}
Candidate key: {EMP-ID, EMP-DEPT}
The table is not in BCNF because neither EMP_DEPT nor EMP_ID alone are keys.
To convert the given table into BCNF, we decompose it into three tables:
EMP_COUNTRY table:

EMP_ID EMP_COUNTRY

264 India

264 India

EMP_DEPT table:

EMP_DEPT DEPT_TYPE EMP_DEPT_NO

Designing D394 283

Testing D394 300

Stores D283 232

Developing D283 549

EMP_DEPT_MAPPING table:

EMP_ID EMP_DEPT

D394 283

D394 300

D283 232

D283 549
 Functional dependencies:
1. EMP_ID → EMP_COUNTRY
2. EMP_DEPT → {DEPT_TYPE, EMP_DEPT_NO}
Candidate keys:
Forthefirsttable: EMP_ID
Forthesecondtable: EMP_DEPT
For the third table: {EMP_ID, EMP_DEPT}
Now, this is in BCNF because left side part of both the functional dependencies is a key.