FUNCTION DEPENDENCY AND TYPES & EXAMPLE
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Functional dependency defines a relationship between attributes in a table where a set of attributes determine another attribute. There are different types of functional dependencies including trivial, non-trivial, multivalued, and transitive. An example given is a student table with attributes Stu_Id, Stu_Name, Stu_Age which has the functional dependency of Stu_Id->Stu_Name since the student ID uniquely identifies the student name.
![• On the other hand, the following dependencies are trivial:
{emp_id, emp_name} -> emp_name [emp_name is a subset of {emp_id, emp_name}]
Completely non trivial FD:
If a Functional dependency X->Y holds true where X intersection Y is Null then this
dependency is said to be completely non trivial function dependency.](https://image.slidesharecdn.com/fd-161021045633/85/FUNCTION-DEPENDENCY-AND-TYPES-EXAMPLE-10-320.jpg)
FUNCTION DEPENDENCY AND TYPES & EXAMPLE
- 1. FUNCTION DEPENDENCY AND TYPES & EXAMPLE NAME-VRAJ PATEL BATCH-A ENROLL NO : 150410107082
- 2. DEFINATION • Functional dependency is a relationship that exists when one attribute uniquely determines another attribute. If R is a relation with attributes X and Y, a functional dependency between the attributes is represented as X->Y, which specifies Y is functionally dependent on X. • The attributes of a table is said to be dependent on each other when an attribute of a table uniquely identifies another attribute of the same table.
- 3. • For example: • Suppose we have a student table with attributes: Stu_Id, Stu_Name, Stu_Age. • Here Stu_Id attribute uniquely identifies the Stu_Name attribute of student table because if we know the student id we can tell the student name associated with it.
- 4. Functional dependency and can be written as : Stu_Id->Stu_Name . we can say Stu_Name is functionally dependent on Stu_Id. Formally: If column A of a table uniquely identifies the column B of same table then it can represented as A->B (Attribute B is functionally dependent on attribute A)
- 5. Types of Functional Dependencies • Trivial functional dependency • Non-trivial functional dependency • Multivalued dependency • Transitive dependency
- 6. Trivial functional dependency • The dependency of an attribute on a set of attributes is known as trivial functional dependency if the set of attributes includes that attribute. Symbolically: • A ->B is trivial functional dependency if B is a subset of A. • The following dependencies are also trivial: A->A & B->B
- 7. • For example: Consider a table with two columns Student_id and Student_Name. {Student_Id, Student_Name} -> Student_Id is a trivial functional dependency as Student_Id is a subset of {Student_Id, Student_Name}. • Also, Student_Id -> Student_Id & Student_Name -> Student_Name are trivial dependencies too.
- 8. Non-trivial functional dependency • If a functional dependency X->Y holds true where Y is not a subset of X then this dependency is called non trivial Functional dependency.
- 9. Example : An employee table with three attributes: emp_id, emp_name, emp_address. The following functional dependencies are non-trivial: emp_id -> emp_name (emp_name is not a subset of emp_id) emp_id -> emp_address (emp_address is not a subset of emp_id)
- 10. • On the other hand, the following dependencies are trivial: {emp_id, emp_name} -> emp_name [emp_name is a subset of {emp_id, emp_name}] Completely non trivial FD: If a Functional dependency X->Y holds true where X intersection Y is Null then this dependency is said to be completely non trivial function dependency.
- 11. Multivalued dependency • Multivalued dependency occurs when there are more than one independent multivalued attributes in a table. • a multivalued dependency is a full constraint between two sets of attributes in a relation. In contrast to the functional dependency, the multivalued dependency requires that certain tuples be present in a relation.
- 12. • Consider a bike manufacture company, which produces two colors (Black and white) in each model every year.
- 13. • Here columns manuf_year and color are independent of each other and dependent on bike_model. In this case these two columns are said to be multivalued dependent on bike_model. These dependencies can be represented like this: • bike_model ->> manuf_year • bike_model ->> color
- 14. Transitive dependency A functional dependency is said to be transitive if it is indirectly formed by two functional dependencies. X -> Z is a transitive dependency if the following three functional dependencies hold true: X->Y Y does not ->X Y->Z A transitive dependency can only occur in a relation of three of more attributes. This dependency helps us normalizing the database in 3NF (3rd Normal Form).
- 15. • Example :-
- 16. • {Book} ->{Author} (if we know the book, we knows the author name) • {Author} does not ->{Book} • {Author} -> {Author_age} • Therefore as per the rule of transitive dependency: • {Book} -> {Author_age} should hold, that makes sense because if we know the book name we can know the author’s age.
- 17. THANK YOU