Armstrong's axioms in DBMS Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What are Armstrong's axioms in database management?

Armstrong's axioms are a set of rules used to infer all functional dependencies on a database relation. They help in reasoning about data dependencies and normalization.

beginner

Name the three basic Armstrong's axioms.

The three basic Armstrong's axioms are:<br>1. Reflexivity<br>2. Augmentation<br>3. Transitivity

beginner

Explain the Reflexivity axiom with an example.

Reflexivity states that if set Y is a subset of set X, then X functionally determines Y (X → Y).<br>Example: If X = {A, B} and Y = {A}, then {A, B} → {A} holds true.

intermediate

What does the Augmentation axiom state?

Augmentation means if X → Y holds, then adding the same set Z to both sides preserves the dependency: XZ → YZ.<br>Example: If {A} → {B}, then {A, C} → {B, C}.

intermediate

Describe the Transitivity axiom with a real-life analogy.

Transitivity says if X → Y and Y → Z, then X → Z.<br>Analogy: If knowing your friend's phone number (X) lets you reach them (Y), and reaching them (Y) lets you get their address (Z), then knowing the phone number (X) lets you get the address (Z).

Which Armstrong's axiom states that if Y is a subset of X, then X determines Y?

A Augmentation

B Transitivity

C Reflexivity

D Decomposition

Reflexivity states that if Y is a subset of X, then X → Y.

If X → Y holds, which axiom allows you to conclude that XZ → YZ also holds?

A Augmentation

B Union

C Transitivity

D Reflexivity

Augmentation allows adding the same set Z to both sides of a functional dependency.

Given X → Y and Y → Z, what can you infer using Armstrong's axioms?

A X → Z

B Z → X

C Y → X

D Z → Y

Transitivity states that if X → Y and Y → Z, then X → Z.

Which of the following is NOT one of the basic Armstrong's axioms?

A Augmentation

B Commutativity

C Transitivity

D Reflexivity

Commutativity is not a basic Armstrong's axiom.

Armstrong's axioms are primarily used for what purpose in databases?

A To manage user permissions

B To create tables

C To write SQL queries

D To infer functional dependencies

Armstrong's axioms help infer all functional dependencies in a relation.

Explain Armstrong's axioms and their importance in database normalization.

Think about how these rules help organize data efficiently.

Describe each of the three basic Armstrong's axioms with simple examples.

Use small sets of attributes to illustrate each axiom.