FD first lesson66666666666666666666.pptx

DB rules

1. Functional Dependency is a key concept in database design that describes a relationship between attributes in a relational database. Specifically, a functional dependency exists when one attribute (or a set of attributes) uniquely determines another attribute (or set of attributes) in a table. Functional Dependency

2. Let A and B be attributes of a table. We say that B is functionally dependent on A (denoted as A→B ,A→B) if, for every unique value of AAA, there is exactly one corresponding value of BBB. For example, if A is a student's ID and B is the student's name, then each student ID uniquely determines a student's name. Therefore, StudentID→StudentNameStudentID \ rightarrow StudentNameStudentID→StudentName is a functional dependency. Definition:

3. Importance in Database Design: Normalization: Functional dependencies are fundamental to the process of normalization, which involves organizing a database to reduce redundancy and improve data integrity. By understanding the functional dependencies in a database, designers can structure the tables to ensure that each piece of data is stored in only one place, reducing the chance of inconsistencies. Data Integrity: Ensuring that functional dependencies are properly defined and enforced helps maintain data integrity. If a database adheres to the principles of functional dependency, it ensures that data is consistent, accurate, and reliable across the database.

4. Importance in Database Design: Avoiding Anomalies: Poorly designed databases can suffer from various anomalies, such as update, insert, and delete anomalies. Functional dependencies help prevent these issues by ensuring that each piece of information is stored in a controlled and logical manner. Efficient Querying: Understanding functional dependencies allows for the creation of more efficient queries. When a database is properly normalized based on functional dependencies, it reduces the need for complex joins and data retrieval operations, improving overall performance. In summary, functional dependency is a critical concept in database design that helps ensure a well-structured, efficient, and reliable database.

5. Functional dependencies (FDs) in database design can be categorized into several types, each serving a different purpose in the normalization process. Here’s an overview of the different types of functional dependencies: 1. Trivial Functional Dependency Definition: A functional dependency A→BA \ rightarrow BA→B is trivial if the set of attributes on the right side is a subset of the set of attributes on the left side. Example: If A={ EmployeeID,EmployeeName }A = \{ EmployeeID , EmployeeName \}A={ EmployeeID,EmployeeName }, then { EmployeeID,EmployeeName }→ EmployeeID \{ EmployeeID , EmployeeName \} \ rightarrow EmployeeID { EmployeeID,EmployeeName }→ EmployeeID is a trivial dependency because EmployeeID is part of the left-hand side. Functional dependencies (FDs types

6. 2. Non-Trivial Functional Dependency Definition: A functional dependency A→BA \ rightarrow BA→B is non-trivial if the set of attributes on the right side is not a subset of the set of attributes on the left side. Example: If A={ EmployeeID }A = \{ EmployeeID \}A={ EmployeeID } and B={ EmployeeName }B = \{ EmployeeName \}B={ EmployeeName }, then EmployeeID→EmployeeNameEmployeeID \ rightarrow EmployeeNameEmployeeID→EmployeeName is a non-trivial dependency because EmployeeName is not a subset of EmployeeID . 3. Full Functional Dependency Definition: A functional dependency A→BA \ rightarrow BA→B is a full dependency if B is fully dependent on A, and removing any attribute from A means B is no longer dependent on A. Example: In a table with a composite primary key { StudentID,CourseID }\{ StudentID , CourseID \}{ StudentID,CourseID }, if StudentID,CourseID→GradeStudentID , CourseID \ rightarrow GradeStudentID,CourseID→Grade and neither StudentID nor CourseID alone determines Grade, then Grade is fully functionally dependent on { StudentID,CourseID }\{ StudentID , CourseID \}{ StudentID,CourseID }. Functional dependencies (FDs types

7. 4. Partial Functional Dependency Definition: A functional dependency A→BA \ rightarrow BA→B is partial if B is dependent on a part of a composite primary key, rather than the entire key. Example: In a table with a composite primary key { StudentID,CourseID }\{ StudentID , CourseID \}{ StudentID,CourseID }, if StudentID→StudentNameStudentID \ rightarrow StudentNameStudentID→StudentName but CourseIDCourseIDCourseID is not needed to determine StudentName , this is a partial dependency. 5. Transitive Dependency Definition: A transitive dependency exists when A→BA \ rightarrow BA→B and B→CB \ rightarrow CB→C imply A→CA \ rightarrow CA→C. It occurs in situations where one attribute depends on another through a third attribute. Example: If StudentID determines Department, and Department determines DepartmentHead , then there is a transitive dependency StudentID→DepartmentHeadStudentID \ rightarrow DepartmentHeadStudentID→DepartmentHead through Department. Functional dependencies (FDs types

8. 6. Multivalued Dependency Definition: A multivalued dependency occurs when one attribute in a table uniquely determines another attribute, but the second attribute can have multiple values for a single value of the first attribute. Example: If EmployeeID determines DependentName , and an employee can have multiple dependents, then EmployeeID multivaluedly determines DependentName . 7. Join Dependency Definition: A join dependency exists if a relation can be divided into two or more tables, which when joined together, recreate the original relation. Example: Consider a relation R with attributes {A,B,C}\{A, B, C\}{A,B,C}. If it can be split into two relations {A,B}\{A, B\}{A,B} and {B,C}\{B, C\}{B,C} that, when joined on B, recreate the original relation R, then R has a join dependency. Functional dependencies (FDs types

9. 8. Embedded Dependency Definition: An embedded dependency is a dependency that holds only within a specific subset of the database rather than the entire database. Example: If a functional dependency holds true only within a certain department of a company, it is considered an embedded dependency. Significance in Database Design: Understanding and Applying: Correctly identifying and applying these dependencies during the normalization process is crucial for minimizing redundancy and ensuring the integrity of the database. Normalization: Many of these dependencies play a role in the normalization process, helping to break down tables into smaller, more manageable pieces without losing important relationships. Functional dependencies (FDs types

10. Quiz on Functional Dependency: Definition and Importance Question 1: Definition of Functional Dependency Q1: Which of the following best describes a functional dependency in a relational database? a) A relationship where one attribute uniquely determines another attribute. b) A constraint that ensures all foreign keys have a corresponding primary key. c) A rule that dictates how many rows a table can have. d) A method for indexing data in a database.

11. Quiz on Functional Dependency: Definition and Importance Answer: a) A relationship where one attribute uniquely determines another attribute.

12. Quiz on Functional Dependency: Definition and Importance Question 2: Example of Functional Dependency Q2: In a table with attributes EmployeeID \text{ EmployeeID } EmployeeID , EmployeeName \text{ EmployeeName } EmployeeName , and Department\text{Department}Department, which of the following functional dependencies is likely to be valid? a) Department→EmployeeName \text{Department} \ rightarrow \text{ EmployeeName } Department→EmployeeName b) EmployeeID→EmployeeName \text{ EmployeeID } \ rightarrow \text{ EmployeeName } EmployeeID→EmployeeName c) EmployeeName→EmployeeID \text{ EmployeeName } \ rightarrow \text{ EmployeeID } EmployeeName→EmployeeID d) Department→EmployeeID \text{Department} \ rightarrow \text{ EmployeeID } Department→EmployeeID

13. Quiz on Functional Dependency: Definition and Importance Answer: b) EmployeeID→EmployeeName \text{ EmployeeID } \ rightarrow \text{ EmployeeName } EmployeeID→EmployeeName

14. Quiz on Functional Dependency: Definition and Importance Question 3: Importance of Functional Dependencies Q3: Why are functional dependencies important in database normalization? a) They help in determining the primary keys of the tables. b) They are used to define indexes in the database. c) They are essential for creating foreign keys. d) They are used to eliminate redundancy and update anomalies.

15. Quiz on Functional Dependency: Definition and Importance Answer: d) They are used to eliminate redundancy and update anomalies.

16. Quiz on Functional Dependency: Definition and Importance Question 4: Functional Dependency and Keys Q4: Which statement is true regarding functional dependencies and candidate keys? a) A candidate key can be determined by a functional dependency. b) A functional dependency can be established only between candidate keys. c) Functional dependencies are irrelevant to candidate keys. d) Functional dependencies are always determined by primary keys only.

17. Quiz on Functional Dependency: Definition and Importance Answer: a) A candidate key can be determined by a functional dependency.

18. Quiz on Functional Dependency: Definition and Importance Question 5: Functional Dependency Violation Q5: Which scenario represents a violation of functional dependency in a database? a) Having duplicate rows in a table. b) A non-key attribute depending on part of a composite key. c) Having multiple tables with the same data. d) A non-key attribute depending on another non-key attribute.

19. Quiz on Functional Dependency: Definition and Importance Answer: d) A non-key attribute depending on another non-key attribute.

20. Quiz on Functional Dependency: Definition and Importance Question 6: Functional Dependency in 1NF Q6: How does functional dependency relate to the First Normal Form (1NF)? a) Functional dependencies are irrelevant to 1NF. b) 1NF ensures that functional dependencies exist. c) 1NF eliminates partial functional dependencies. d) 1NF requires that every column must be functionally dependent on the primary key.

21. Quiz on Functional Dependency: Definition and Importance Answer: d) 1NF requires that every column must be functionally dependent on the primary key.

22. Quiz on Types of Functional Dependencies Question 1: Full Functional Dependency Q1: Which of the following scenarios describes a full functional dependency? a) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C, but A↛CA \ nrightarrow CA↛C and B↛CB \ nrightarrow CB↛C b) A→CA \ rightarrow CA→C and B→CB \ rightarrow CB→C c) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C, and A→CA \ rightarrow CA→C d) A→B→CA \ rightarrow B \ rightarrow CA→B→C

23. Quiz on Types of Functional Dependencies Answer: a) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C, but A↛CA \ nrightarrow CA↛C and B↛CB \ nrightarrow CB↛C

24. Quiz on Types of Functional Dependencies Question 2: Partial Functional Dependency Q2: Which of the following is an example of a partial functional dependency? a) A→BA \ rightarrow BA→B, but B↛AB \ nrightarrow AB↛A b) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C, and A→CA \ rightarrow CA→C c) A→{B,C}A \ rightarrow \{B, C\}A→{B,C} d) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C, but B→CB \ rightarrow CB→C

25. Quiz on Types of Functional Dependencies Answer: b) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C, and A→CA \ rightarrow CA→C

26. Quiz on Types of Functional Dependencies Question 3: Transitive Dependency Q3: Which of the following is an example of a transitive dependency? a) A→B→CA \ rightarrow B \ rightarrow CA→B→C b) A→BA \ rightarrow BA→B, B→CB \ rightarrow CB→C, so A→CA \ rightarrow CA→C c) A→BA \ rightarrow BA→B, but B↛CB \ nrightarrow CB↛C d) A→CA \ rightarrow CA→C, regardless of BBB

27. Quiz on Types of Functional Dependencies Answer: b) A→BA \ rightarrow BA→B, B→CB \ rightarrow CB→C, so A→CA \ rightarrow CA→C

28. Quiz on Types of Functional Dependencies Question 4: Trivial Functional Dependency Q4: Which of the following is an example of a trivial functional dependency? a) A→AA \ rightarrow AA→A b) A→BA \ rightarrow BA→B c) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C d) A→{B,C}A \ rightarrow \{B, C\}A→{B,C}

29. Quiz on Types of Functional Dependencies Answer: a) A→AA \ rightarrow AA→A

30. Quiz on Types of Functional Dependencies Question 5: Non-trivial Functional Dependency Q5: Which scenario describes a non-trivial functional dependency? a) A→AA \ rightarrow AA→A b) A→BA \ rightarrow BA→B c) A→{A,B}A \ rightarrow \{A, B\}A→{A,B} d) B→BB \ rightarrow BB→B

31. Quiz on Types of Functional Dependencies Answer: b) A→BA \ rightarrow BA→B

32. Quiz on Types of Functional Dependencies Question 6: Multivalued Dependency Q6: Which of the following scenarios best describes a multivalued dependency? a) A→BA \ rightarrow BA→B and A→CA \ rightarrow CA→C, with BBB and CCC independent of each other b) A→{B,C}A \ rightarrow \{B, C\}A→{B,C} c) {A,B}→C\{A, B\} \ rightarrow C{A,B}→C d) A→BA \ rightarrow BA→B, B→CB \ rightarrow CB→C

33. Quiz on Types of Functional Dependencies Answer: a) A→BA \ rightarrow BA→B and A→CA \ rightarrow CA→C, with BBB and CCC independent of each other

34. Quiz on Types of Functional Dependencies Question 7: Join Dependency Q7: Which of the following describes a join dependency? a) A dependency where a table can be decomposed into two or more tables and then joined back without loss of information. b) A dependency where one attribute is dependent on another. c) A dependency that occurs only when foreign keys are used. d) A dependency that involves partial functional dependencies.

35. Quiz on Types of Functional Dependencies Answer: a) A dependency where a table can be decomposed into two or more tables and then joined back without loss of information.