Functional dependency explained.

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Functional dependency

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In the context of relational databases, a functional dependency is a relationship between two or more attributes (or columns) in a table where the value of one attribute determines the value of another.

For example, if we have a table called “Students” with the columns “Student_ID,” “First_Name,” “Last_Name,” and “Email,” we can say that the attribute “Email” is functionally dependent on the attributes “First_Name” and “Last_Name.” This is because the value of the “Email” attribute is determined by the values of the “First_Name” and “Last_Name” attributes.

In general, a functional dependency is represented as A -> B, where A is the determinant (or independent) attribute and B is the dependent attribute. This means that for any given value of A, there is only one possible value of B.

Functional dependencies are important in database design because they help ensure data integrity and minimize redundancy. By identifying and removing redundant data, we can make our databases more efficient and easier to manage.

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describe its type too with example

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There are several types of functional dependencies in a database. The main types are:

1. Trivial Functional Dependency: A functional dependency A -> B is trivial if B is a subset of A. For example, in a table with columns “Student_ID,” “First_Name,” and “Last_Name,” the functional dependency “Student_ID, First_Name -> First_Name” is trivial because First_Name is already a part of the determinant.
2. Non-Trivial Functional Dependency: A functional dependency A -> B is non-trivial if B is not a subset of A. For example, in a table with columns “Student_ID,” “First_Name,” “Last_Name,” and “Email,” the functional dependency “First_Name, Last_Name -> Email” is non-trivial because the Email attribute is not a part of the determinant.
3. Transitive Functional Dependency: A functional dependency A -> B and B -> C implies a transitive functional dependency A -> C. For example, in a table with columns “Student_ID,” “First_Name,” “Last_Name,” and “City,” the functional dependency “Student_ID -> City” and “City -> State” imply a transitive functional dependency “Student_ID -> State”.
4. Partial Dependency: A functional dependency A -> B is a partial dependency if B is functionally dependent on a proper subset of A. For example, in a table with columns “Student_ID,” “First_Name,” “Last_Name,” and “Email,” the functional dependency “Student_ID, First_Name, Last_Name -> Email” is a partial dependency because the attribute Email is also functionally dependent on just the subset “Student_ID”.
5. Full Dependency: A functional dependency A -> B is a full dependency if B is functionally dependent on the entire set of A. For example, in a table with columns “Student_ID,” “First_Name,” “Last_Name,” and “Email,” the functional dependency “Student_ID, First_Name, Last_Name -> Email” is a full dependency because the attribute Email is functionally dependent on the entire set of “Student_ID”, “First_Name”, and “Last_Name”.

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Normalizations and its forms, with example and tabels

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Normalization is the process of organizing data in a database to reduce data redundancy and dependency, making the database more efficient, easier to maintain, and less prone to errors. There are different normal forms in which data can be organized. The most commonly used normal forms are:

1. First Normal Form (1NF): A table is in 1NF if it has no repeating groups or arrays, meaning that each column of the table contains only atomic values. For example, consider the following table called “Student_Info”:

Student_ID	First_Name	Last_Name	Course_List
1	John	Smith	Math, Science, English
2	Jane	Doe	Math, Science, History, French

This table is not in 1NF because the “Course_List” column contains multiple values, which can be split into separate rows. We can normalize this table to 1NF by splitting the “Course_List” column into separate rows and creating a new table called “Course_Info”:

Student_ID	First_Name	Last_Name
1	John	Smith
2	Jane	Doe

Student_ID	Course
1	Math
1	Science
1	English
2	Math
2	Science
2	History
2	French

1. Second Normal Form (2NF): A table is in 2NF if it is in 1NF and every non-key attribute is fully functionally dependent on the primary key. For example, consider the following table called “Order_Details”:

Order_ID	Product_ID	Product_Name	Product_Price	Quantity
1001	P001	iPhone X	999	2
1001	P002	AirPods	149	3
1002	P001	iPhone X	999	1
1002	P003	MacBook Pro	1499	1

This table is not in 2NF because the “Product_Name” and “Product_Price” columns are dependent only on the “Product_ID” column, which is not a primary key. We can normalize this table to 2NF by creating a new table called “Product_Info”:

Product_ID	Product_Name	Product_Price
P001	iPhone X	999
P002	AirPods	149
P003	MacBook Pro	1499

Order_ID	Product_ID	Quantity
1001	P001	2
1001	P002	3
1002	P001	1
1002	P003	1

1. Third Normal Form (3NF): A table is in 3NF if it is in 2NF and has no transitive dependencies. For example, consider the following table called “Employee_Details”:

Employee_ID	Employee_Name	Department_ID	Department_Name	Manager_ID
E001	John Smith	D001	Sales

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complete from Third Normal Form

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Continuing from the previous answer:

Employee_ID	Employee_Name	Department_ID	Manager_ID
E001	John Smith	D001	M001
E002	Jane Doe	D001	M001
E003	Bob Johnson	D002	M002

Department_ID	Department_Name	Manager_ID
D001	Sales	M001
D002	Marketing	M002

Manager_ID	Manager_Name
M001	Jack Johnson
M002	Sarah Thompson

This table is not in 3NF because the “Department_Name” and “Manager_Name” columns are not directly dependent on the primary key “Employee_ID”. We can normalize this table to 3NF by creating new tables called “Department_Info” and “Manager_Info”:

Employee_ID	Employee_Name	Department_ID
E001	John Smith	D001
E002	Jane Doe	D001
E003	Bob Johnson	D002

Department_ID	Manager_ID
D001	M001
D002	M002

Manager_ID	Manager_Name
M001	Jack Johnson
M002	Sarah Thompson

Department_ID	Department_Name
D001	Sales
D002	Marketing

This new design eliminates the transitive dependency and breaks down the original table into smaller, more manageable tables.

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and give for BCNF

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Boyce-Codd Normal Form (BCNF) is a stricter form of normalization that ensures that every determinant in a table is a candidate key. A determinant is any attribute or combination of attributes that determines the values of other attributes in a table. A candidate key is a minimal set of attributes that can uniquely identify each row in a table. A table is in BCNF if and only if every determinant is a candidate key.

For example, consider the following table called “Employee_Project”:

Employee_ID	Project_ID	Project_Name	Department_ID
E001	P001	Project A	D001
E001	P002	Project B	D001
E002	P001	Project A	D001
E003	P003	Project C	D002

In this table, the determinant is the combination of “Employee_ID” and “Project_ID”, and it determines the values of “Project_Name” and “Department_ID”. However, “Department_ID” is not dependent on the candidate key “Employee_ID” alone, but on the combination of “Employee_ID” and “Project_ID”. Therefore, this table is not in BCNF.

To normalize this table to BCNF, we can create two new tables called “Employee_Project_Info” and “Department_Info”:

Employee_ID	Project_ID
E001	P001
E001	P002
E002	P001
E003	P003

Project_ID	Project_Name
P001	Project A
P002	Project B
P003	Project C

Department_ID	Project_ID
D001	P001
D001	P002
D002	P003

Now, each table is in BCNF as each determinant is a candidate key. This design also eliminates data redundancy and dependency, making the database more efficient and easier to maintain.

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difference between 3NF and BCNF with suitable example

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Both Third Normal Form (3NF) and Boyce-Codd Normal Form (BCNF) are forms of database normalization that aim to eliminate data redundancy and dependency. However, BCNF is a stricter form of normalization than 3NF.

In 3NF, a table must satisfy the following conditions:

1. It is in second normal form (2NF)
2. It does not have transitive dependencies

A transitive dependency is a functional dependency between two non-key attributes, where one non-key attribute depends on another non-key attribute, which in turn depends on the primary key.

For example, consider the following table called “Customer_Orders”:

Customer_ID	Order_ID	Order_Date	Product_Name	Product_Price
C001	O001	2021-01-01	Product A	$10
C001	O001	2021-01-01	Product B	$20
C002	O002	2021-01-02	Product C	$30

In this table, “Product_Name” and “Product_Price” are dependent on “Order_ID”, but “Order_ID” is not a candidate key. Instead, “Customer_ID” and “Order_ID” together form a composite primary key. Therefore, this table is not in 3NF as it has a transitive dependency between “Order_ID” and “Product_Name”/“Product_Price”.

To normalize this table to 3NF, we can create two new tables called “Order_Info” and “Product_Info”:

Customer_ID	Order_ID	Order_Date
C001	O001	2021-01-01
C002	O002	2021-01-02

Order_ID	Product_Name
O001	Product A
O001	Product B
O002	Product C

Product_Name	Product_Price
Product A	$10
Product B	$20
Product C	$30

On the other hand, in BCNF, a table must satisfy the following condition:

1. Every determinant is a candidate key

A determinant is any attribute or combination of attributes that determines the values of other attributes in a table. A candidate key is a minimal set of attributes that can uniquely identify each row in a table.

For example, consider the following table called “Employee_Project”:

Employee_ID	Project_ID	Project_Name	Department_ID
E001	P001	Project A	D001
E001	P002	Project B	D001
E002	P001	Project A	D001
E003	P003	Project C	D002

In this table, the determinant is the combination of “Employee_ID” and “Project_ID”, and it determines the values of “Project_Name” and “Department_ID”. However, “Department_ID” is not dependent on the candidate key “Employee_ID” alone, but on the combination of “Employee_ID” and “Project_ID”. Therefore, this table is not in BCNF.

To normalize this table to BCNF, we can create two new tables called “Employee_Project_Info” and “Department_Info”, as shown in the previous example.

In summary, the main difference between 3NF and BCNF is that BCNF

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In summary, the main difference between 3NF and BCNF is that BCNF

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requires every determinant in a table to be a candidate key, whereas 3NF only requires that a table does not have transitive dependencies. BCNF is a stricter form of normalization than 3NF and leads to a more optimized database design.