Canonical cover in DBMS Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define a canonical cover in database theory.

DBMS Theory

A canonical cover is a minimal set of functional dependencies that is [1] to the original set.

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Aequivalent

Blarger

Cunrelated

Dsimpler

Attempts:

3 left

💡 Hint

Common Mistakes

Thinking the canonical cover is larger than the original set.

Confusing equivalence with simplification only.

A canonical cover is a minimal set of functional dependencies that is equivalent to the original set, meaning it preserves the same closure.

2fill in blank

medium

Complete the code to describe a step in finding a canonical cover.

DBMS Theory

One step in finding a canonical cover is to [1] extraneous attributes from functional dependencies.

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Aadd

Bduplicate

Cignore

Dremove

Attempts:

3 left

💡 Hint

Common Mistakes

Trying to add attributes instead of removing them.

Ignoring extraneous attributes and not simplifying.

Removing extraneous attributes helps simplify the functional dependencies without changing their meaning.

3fill in blank

hard

Fix the error in the statement about canonical cover.

DBMS Theory

A canonical cover must have [1] functional dependencies than the original set.

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Afewer

Brandom

Cequal

Dmore

Attempts:

3 left

💡 Hint

Common Mistakes

Assuming the canonical cover has more dependencies.

Confusing minimal with random or equal.

A canonical cover has fewer or equal functional dependencies, but it is minimal, so usually fewer.

4fill in blank

hard

Fill both blanks to complete the process of canonical cover simplification.

DBMS Theory

To simplify, first [1] the right side of dependencies to single attributes, then [2] extraneous attributes from the left side.

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Adecompose

Bcombine

Cremove

Dadd

Attempts:

3 left

💡 Hint

Common Mistakes

Combining right sides instead of decomposing.

Adding attributes instead of removing extraneous ones.

Decomposing the right side ensures each dependency has a single attribute on the right. Then removing extraneous attributes from the left side simplifies the dependencies.

5fill in blank

hard

Fill all three blanks to complete the canonical cover definition code snippet.

DBMS Theory

canonical_cover = [1]: [2] for [3] in functional_dependencies if not is_redundant([3])}

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Afd.left_side

Bfd.right_side

Cfd

Dfd.attributes

Attempts:

3 left

💡 Hint

Common Mistakes

Using attributes instead of left or right sides.

Using wrong variable names causing errors.

This code creates a dictionary where keys are the left sides of functional dependencies, values are the right sides, and only includes dependencies that are not redundant.

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