Lecture on Functional Dependency

Introduction

• Functional dependency is crucial for understanding normalization in database management systems (DBMS).
• It's essential to grasp the basics of functional dependency to understand normalization and normal forms.
• The lecture provides an explanation of functional dependency with examples.

Definition

• Functional Dependency (FD): A relationship where one attribute (or a set of attributes) determines another attribute.
• Notation: Represented by an arrow, e.g., X → Y, implying Y is functionally dependent on X.

Explanation

• If you know the value of X, you can find the value of Y from the table, not by computation but by searching.
• X is known as the determinant and Y as the dependent.
• For a set of tuples, if X values are the same, Y values must be the same for FD to exist.

Examples and Rules

• Example 1:

  • Relation R with attributes X and Y.
  • If X = 2 in the table, Y could be determined if it's uniquely associated with X.
  • If duplicate X values exist with different Y values, it's not a FD.

• Mathematical Analogy: Like y = x² + 5x, Y is dependent on X.

• In DBMS, you search for Y using X values, not compute.

Key Rule

• If in two tuples, T1.x = T2.x, then it must hold that T1.y = T2.y for FD to exist.

Practical Example

• Relation: Students with attributes roll number, name, marks, department, and course.
• Checking FD:
  • Roll number → Name: No repetitions in roll number imply a FD.
  • Name → Roll number: Possible only if names uniquely determine roll numbers.
  • Department → Course: Not a FD if the same department has different courses.

Set of Attributes

• X and Y can be sets of attributes, not just single ones.
• Example: Roll number and name together determining marks.

Additional Considerations

• Roll number can uniquely identify students, hence a FD exists.
• Name may not uniquely identify students if duplicate names exist.

Complex Functional Dependencies

• Multiple attributes can determine a set of other attributes.
• Example: (Name, Marks) → Department, Course.
• Must check all combinations and ensure consistency.

Conclusion

• Functional dependency is defined by uniformity in dependent values when determinant values match.
• Practice problems can be used to test understanding of FDs in various relations.

Next Steps

• Next lecture will cover types of functional dependencies and Armstrong's axioms, which are properties of FDs.