Functional Dependency Lecture Notes

Introduction

• Topic: Functional Dependency
• Context: Understanding normal forms (1NF, 2NF, 3NF, BCNF)
• Reminder: Covered normalization and denormalization in previous lectures.

Definition of Functional Dependency

• Functional dependency describes the relationship between attributes in a relation (table).
• Example from math: If y = f(x) (e.g., y = x² + 2x + 1), then y is functionally dependent on x.

Key Concepts

• Attributes: Columns in a table.
• Relation: A table in a database.
• Functional Dependency: If knowing the value of x allows us to determine the value of y, then y is functionally dependent on x.
• Not limited to single attributes; can involve sets of attributes.
• Primary Key: A unique identification key, which can be a single or composite attribute.
• Determinant: The attribute (or set of attributes) that can uniquely determine another attribute.

Examples

• In a table with attributes Roll Number and Name:

  • If Roll Number is known, Name can be determined, thus Name is functionally dependent on Roll Number.

• Table Example:

  Employee ID	First Name	Last Name
  1	Ria	Singh
  1	Rahul	Kumar

  • Here, Employee ID does not uniquely determine First Name because multiple names correspond to the same ID.

Identifying Functional Dependencies

• For a relation with attributes x and y, if x determines y, then for any two records with the same value of x, the corresponding values of y must be the same.
• If duplicates exist in the Employee ID, check whether values of First Name and Last Name are consistent for the same ID.

Properties of Functional Dependency (Inference Rules)

1. Reflexivity: If Y is a subset of X, then X determines Y.
2. Augmentation: If X determines Y, then X, Z determines Y, Z for any Z.
3. Transitivity: If X determines Y and Y determines Z, then X determines Z.
4. Union: If X determines Y and X determines Z, then X determines Y, Z.
5. Decomposition: If X determines Y, Z, then X determines Y and X determines Z.

Types of Functional Dependency

• Trivial Functional Dependency: X determines Y is trivial if Y is a subset of X. Example: Employee ID determines Employee ID.
• Non-Trivial Functional Dependency: X determines Y is non-trivial if Y is not a subset of X. Example: Employee Name determining Employee ID needs to be verified by checking the data table.

Conclusion

• Summary of functional dependency and its importance in understanding database normalization.
• Encouragement to follow the channel for more content and to engage with the material.