Functional Dependencies (FDs)

1. Definition

• A functional dependency (FD) describes a relationship between attributes in a relation.
• If attribute X determines attribute Y, it is written as:
  • X → Y
• This means that if two tuples have the same value for X, they must have the same value for Y.

2. Types of FDs

1. Trivial FD:
   • When Y is a subset of X.
   • Example: {StudentID, Name} → Name.
2. Non-Trivial FD:
   • When Y is not a subset of X.
   • Example: StudentID → Name.
3. Fully Functional Dependency:
   • All attributes in X are necessary to determine Y.
   • Example: {StudentID, CourseID} → Grade.
4. Transitive Dependency:
   • If X → Y and Y → Z, then X → Z.
   • Example: StudentID → DepartmentID, DepartmentID → DepartmentName.

Decomposition Using FDs

1. Purpose of Decomposition

Decomposition breaks a relation into smaller relations to:

• Eliminate redundancy.
• Ensure lossless decomposition.
• Preserve dependencies.