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In a relational database management system, a functional dependency describes the relationship between two sets of attributes where one set determines the value of another. It is written as 𝑋→𝑌, where 𝑋 (the attribute set on the left) is known as the Determinant, and 𝑌 (the attribute set on the right) is known as the Dependent.

Functional dependencies help understand how attributes relate to each other in a database, which is crucial for database design and normalization.

Types of Functional Dependency

Full Functional Dependency

A functional dependency 𝑋→𝑌 is a full functional dependency if removing any attribute from 𝑋 means the dependency no longer holds. In simpler terms, 𝑌 depends entirely on 𝑋.

Example: If we have a table Enrollment(StudentID, CourseID, Grade), the dependency (StudentID, CourseID) → Grade is a full functional dependency because neither StudentID nor CourseID alone can determine the Grade.

Partial Functional Dependency

A partial functional dependency occurs when only part of a composite primary key determines a non-key attribute.

Example: In a table Enrollment(StudentID, CourseID, StudentName), StudentName depends only on StudentID and not the entire composite key (StudentID, CourseID). This is a partial functional dependency.

Trivial Functional Dependency

A trivial functional dependency happens when the dependent attribute is already part of the determinant attribute set.

Example: {Roll no., Name} → {Name} is a trivial functional dependency because Name is already part of the determinant (Roll no., Name).

Non-trivial Functional Dependency

A non-trivial functional dependency occurs when the dependent attribute is not part of the determinant attribute set.

Example: {Roll no., Name} → {Dept name} is a non-trivial functional dependency because Dept name is not part of {Roll no., Name}.

Transitive Dependency

A transitive dependency happens when there is an indirect relationship between attributes. If A → B and B → C, then A → C is a transitive dependency.

Example: If Roll no. → Dept name and Dept name → Dept building, then Roll no. → Dept building is a transitive dependency.

Multivalued Dependency

In a multivalued dependency, the dependent attributes are independent of each other. If A → {B, C}, and there is no relati