Functional Dependencies and Normalization Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Functional Dependencies and Normalization notes for GATE DA: 36 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questions.

Chapter Roadmap: Functional Dependencies and Normalization

Chapter Roadmap

Functional Dependencies and Candidate Keys

The foundation. Decoding the rules of data determination and systematically extracting minimal keys.

Normalization, BCNF and Dependency Preservation

The application. Breaking down messy tables into clean structures to eliminate update anomalies.

Armstrong Axioms and Derived Dependencies

The proof. Mastering the formal mathematical rules to verify and derive functional dependencies.

Functional Dependencies and Candidate Keys

A database without defined dependencies is just a chaotic bucket of text. These rules capture real-world semantics, ensuring data is logically connected and uniquely identifiable.

What you will learn here

The precise definition and intuition behind Functional Dependencies.
How to compute the closure of an attribute set.
The systematic, foolproof method to find all Candidate Keys.
How to distinguish between Super Keys, Candidate Keys, and Prime Attributes.

Context: This is the starting point of database design. We must understand the rules before we can normalize the tables.

The Intuition Behind Functional Dependencies

The Core Intuition

A Functional Dependency (FD) is a constraint between two sets of attributes in a relation. It captures a real-world rule of determination.

The "If-Then" Rule

If I know the value of set $X$ , I can uniquely determine the value of set $Y$ .

Example: If I know a StudentID, I can uniquely determine the StudentName.
Notation: We write this as $X \to Y$ .

Crucial Detail

This is a constraint on all valid instances of the relation. It is not just a pattern observed in the current data snapshot; it is a semantic rule that must hold true for any past, present, or future data.

Trivial vs Non-Trivial Dependencies

Classifying Functional Dependencies

Trivial Dependencies

Definition: $X \to Y$ is trivial if $Y \subseteq X$ .

Example: ${A, B} \to A$ is trivial because $A$ is already part of the left side.

Significance: Always true by definition; provides zero new information.

Non-Trivial Dependencies

Definition: $X \to Y$ is non-trivial if $Y \neq \subseteq X$ .

Example: $A \to B$ is non-trivial.

Significance: Represents actual, meaningful business rules and constraints.

Completely Non-Trivial

Definition: $X \cap Y = \emptyset$ (The left and right sides share absolutely no attributes).

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Functional Dependencies and Normalization Notes for GATE DA: Concepts, Formulas, Worked Examples & Practice

Functional Dependencies and Normalization notes for GATE DA: 36 study cards covering concepts, formulas, shortcuts and exam traps, plus solved practice questi

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