Canonical cover in DBMS Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

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

Choose the best description of the main purpose of a canonical cover for a set of functional dependencies.

A To list all possible functional dependencies in a relation

B To maximize the number of functional dependencies for better normalization

C To remove all keys from the set of functional dependencies

D To find a minimal set of functional dependencies that is equivalent to the original set

💡 Hint

Think about simplifying the set of dependencies without changing what they represent.

A canonical cover is a minimal set of functional dependencies that preserves the original dependencies' meaning. It removes redundancy and simplifies analysis.

📋 Factual

intermediate

Which step is NOT part of finding a canonical cover?

Select the step that is not involved in computing a canonical cover.

A Add new functional dependencies to increase coverage

B Remove extraneous attributes from the left side of dependencies

C Remove redundant functional dependencies

D Decompose functional dependencies with multiple attributes on the right side into single attributes

💡 Hint

Consider whether adding dependencies helps simplify or complicate the set.

Finding a canonical cover involves simplifying and reducing dependencies, not adding new ones.

🔍 Analysis

advanced

What is the canonical cover of the following set of functional dependencies?

F = { A -> BC, B -> C, A -> B, AB -> C }

Identify the canonical cover of the given functional dependencies.

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

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

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

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

💡 Hint

Try to remove redundant dependencies and extraneous attributes step by step.

Decompose A -> BC into A -> B and A -> C. Since B -> C exists, A -> C is redundant. Also, AB -> C is redundant because A -> B and B -> C imply AB -> C. So the minimal set is { A -> B, B -> C }.

❓ Reasoning

advanced

Why is it important to remove extraneous attributes from the left side of a functional dependency when computing a canonical cover?

Choose the best explanation for removing extraneous attributes from the left side of dependencies.

A To make the left side contain all attributes of the relation

B To increase the number of dependencies for better normalization

C To ensure the dependency is minimal and does not contain unnecessary attributes

D To convert the dependency into a multivalued dependency

💡 Hint

Think about what 'extraneous' means in this context.

Removing extraneous attributes makes the dependency minimal, which helps simplify the set and avoid redundancy.

❓ Comparison

expert

Compare the sets of functional dependencies before and after computing the canonical cover.

Given F = { A -> BC, B -> C, A -> B, AB -> C }, which statement is true?

Choose the correct statement about the relationship between the original set and its canonical cover.

A The canonical cover has more dependencies and a larger closure than the original set

B The canonical cover has fewer dependencies but represents the same closure as the original set

C The canonical cover removes some dependencies and changes the closure

D The canonical cover is identical to the original set

💡 Hint

Recall what equivalence means in terms of functional dependencies.

A canonical cover is a minimal equivalent set of dependencies that has the same closure as the original set but fewer dependencies.