Canonical cover in DBMS Theory - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a canonical cover in database theory?

A canonical cover is a simplified set of functional dependencies that is equivalent to the original set but has no redundant dependencies or attributes.

beginner

Why do we use a canonical cover?

We use a canonical cover to make the set of functional dependencies easier to work with by removing redundancies, which helps in database normalization and design.

intermediate

What are the main steps to find a canonical cover?

1. Split dependencies with multiple attributes on the right side into single attributes.
2. Remove extraneous attributes from left and right sides.
3. Remove redundant dependencies.

intermediate

What does it mean to remove an extraneous attribute?

Removing an extraneous attribute means eliminating an attribute from a functional dependency if it can be inferred from other dependencies without changing the overall meaning.

beginner

How does a canonical cover help in database normalization?

A canonical cover helps by providing a minimal and clear set of dependencies, making it easier to identify keys and design tables that avoid redundancy and update anomalies.

What is the first step in finding a canonical cover?

A Removing extraneous attributes from the left side

B Removing redundant dependencies

C Splitting dependencies with multiple attributes on the right side

D Combining all dependencies into one

The first step is to split dependencies that have multiple attributes on the right side into separate dependencies with single attributes.

Which of the following is NOT a goal of a canonical cover?

A Add more dependencies for clarity

B Remove redundant dependencies

C Remove extraneous attributes

D Simplify the set of functional dependencies

A canonical cover aims to simplify and reduce dependencies, not add more.

What does it mean if an attribute is extraneous in a functional dependency?

A It can be removed without changing the dependency's meaning

B It is a key attribute

C It is the only attribute on the right side

D It is necessary for the dependency

An extraneous attribute can be removed without affecting the overall set of dependencies.

Why is a canonical cover important for database normalization?

A It merges all tables into one

B It increases the number of tables

C It removes all functional dependencies

D It helps identify keys and avoid redundancy

A canonical cover helps identify keys and design tables that avoid redundancy and anomalies.

Which step comes after removing extraneous attributes when finding a canonical cover?

A Splitting dependencies

B Removing redundant dependencies

C Adding new dependencies

D Normalizing tables

After removing extraneous attributes, the next step is to remove redundant dependencies.

Explain what a canonical cover is and why it is useful in database design.

Think about how simplifying dependencies helps organize data better.

Describe the main steps involved in finding a canonical cover from a set of functional dependencies.

Consider the process of making dependencies minimal and clear.

Practice

1. What is the main purpose of a canonical cover in database design?

easy

A. To simplify and minimize the set of functional dependencies

B. To increase the number of functional dependencies

C. To add redundant dependencies for safety

D. To create more complex database schemas

Solution

1. Step 1: Understand the definition of canonical cover

   A canonical cover is a minimal set of functional dependencies that preserves the original dependencies without redundancy.

2. Step 2: Identify the purpose in database design

   It simplifies the design by removing redundant dependencies and splitting dependencies with multiple attributes on the right side.

3. Final Answer:

   To simplify and minimize the set of functional dependencies -> Option A

4. Quick Check:

   Canonical cover = minimal functional dependencies [OK]

Hint: Canonical cover means minimal and simple dependencies [OK]

Common Mistakes:

• Thinking it adds more dependencies
• Confusing it with normalization
• Assuming it complicates the schema

2. Which of the following is the correct step when creating a canonical cover?

easy

A. Remove extraneous attributes from dependencies

B. Add extra attributes to the left side

C. Combine all dependencies into one

D. Ignore dependencies with single attributes

Solution

1. Step 1: Recall the process of forming a canonical cover

   One key step is to remove extraneous attributes from the left or right side of functional dependencies to simplify them.

2. Step 2: Evaluate the options

   Removing extraneous attributes is correct, while adding extra attributes or ignoring dependencies is incorrect.

3. Final Answer:

   Remove extraneous attributes from dependencies -> Option A

4. Quick Check:

   Remove extraneous attributes = canonical cover step [OK]

Hint: Remove unnecessary parts to simplify dependencies [OK]

Common Mistakes:

• Adding attributes instead of removing
• Merging all dependencies incorrectly
• Ignoring single attribute dependencies

3. Given the functional dependencies:
F = { A -> BC, B -> C, A -> B }
What is the canonical cover of F?

medium

A. { A -> B, A -> C }

B. { A -> BC, B -> C }

C. { A -> B, B -> C }

D. { A -> B, B -> C, A -> C }

Solution

1. Step 1: Split dependencies with multiple attributes on right

   Split A -> BC into A -> B and A -> C.

2. Step 2: Remove redundant dependencies

   Since B -> C exists, and A -> B exists, A -> C is implied and redundant.

3. Final Answer:

   { A -> B, B -> C } -> Option C

4. Quick Check:

   Canonical cover removes redundant dependencies [OK]

Hint: Split right side, then remove implied dependencies [OK]

Common Mistakes:

• Not splitting multi-attribute dependencies
• Keeping redundant dependencies
• Confusing implied dependencies

4. Identify the error in this canonical cover step:
F = { A -> BC, B -> C }
Step: Remove C from A -> BC because B -> C exists.
Is this step correct?

medium

A. No, because C is not extraneous in A -> BC

B. Yes, because C is extraneous in A -> BC

C. Yes, because B -> C covers C

D. No, because B -> C is unrelated

Solution

1. Step 1: Check if C is extraneous in A -> BC

   Since B -> C exists, C can be derived from B, so C is extraneous on the right side of A -> BC.

2. Step 2: Confirm correctness of removal

   Removing C from A -> BC to get A -> B is valid and simplifies the dependencies.

3. Final Answer:

   Yes, because C is extraneous in A -> BC -> Option B

4. Quick Check:

   Extraneous attribute removal is valid [OK]

Hint: If attribute can be derived, it's extraneous [OK]

Common Mistakes:

• Thinking all right-side attributes are essential
• Ignoring dependency chains
• Confusing extraneous with essential attributes

5. You have the dependencies:
F = { AB -> C, A -> B, B -> C }
What is the canonical cover of F?

hard

A. { A -> B, AB -> C }

B. { AB -> C, A -> B }

C. { A -> B, B -> C, AB -> C }

D. { A -> B, B -> C }

Solution

1. Step 1: Check for extraneous attributes on left side

   In AB -> C, check if A or B is extraneous. Since B -> C exists, A is extraneous.

2. Step 2: Simplify AB -> C to B -> C and remove redundant dependencies

   Now F becomes { A -> B, B -> C }. This set is minimal and covers all dependencies.

3. Final Answer:

   { A -> B, B -> C } -> Option D

4. Quick Check:

   Remove extraneous left attributes and redundant dependencies [OK]

Hint: Remove extraneous left attributes to simplify [OK]

Common Mistakes:

• Not checking left side for extraneous attributes
• Keeping redundant dependencies
• Assuming all attributes on left are needed