Boyce-Codd Normal Form (BCNF) in DBMS Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to identify a candidate key in a relation.

DBMS Theory

A candidate key is a minimal set of attributes [1] uniquely identify tuples in a relation.

Drag options to blanks, or click blank then click option'

Awhere

Bthat

Cwhen

Dwhich

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'which' instead of 'that' can change the meaning.

The phrase 'a minimal set of attributes that uniquely identify tuples' correctly describes a candidate key.

2fill in blank

medium

Complete the sentence to explain BCNF condition.

DBMS Theory

A relation is in BCNF if for every functional dependency X [1] Y, X is a superkey.

Drag options to blanks, or click blank then click option'

A=

B<-

C<->

D->

Attempts:

3 left

💡 Hint

Common Mistakes

Using '<-' reverses the dependency direction.

The arrow '->' denotes a functional dependency from X to Y.

3fill in blank

hard

Fix the error in the BCNF definition.

DBMS Theory

In BCNF, every determinant [1] a superkey.

Drag options to blanks, or click blank then click option'

Ais

Bare

Cbe

Dwas

Attempts:

3 left

💡 Hint

Common Mistakes

Using plural verb 'are' with singular subject.

'Determinant' is singular, so the verb must be 'is'.

4fill in blank

hard

Fill in the blank to complete the BCNF condition statement.

DBMS Theory

If a relation has a functional dependency [1], then the left side must be a superkey.

Drag options to blanks, or click blank then click option'

AX -> Y

BX <- Y

CX = Y

DX <-> Y

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect symbols like '<-' or '=' for functional dependencies.

The functional dependency is represented as 'X -> Y'.

5fill in blank

hard

Fill all three blanks to complete the BCNF example code snippet.

DBMS Theory

relation = { 'attributes': ['A', 'B'], 'functional_dependencies': [('[1]', '[2]')], 'candidate_keys': ['[3]'] }

Drag options to blanks, or click blank then click option'

AA

BB

CAB

DC

Attempts:

3 left

💡 Hint

Common Mistakes

Confusing single attributes with candidate keys which can be multiple attributes.

The functional dependency is from 'A' to 'B', and the candidate key is 'A' which uniquely identifies tuples.

Practice

1. What is the main goal of Boyce-Codd Normal Form (BCNF) in database design?

easy

A. To ensure every functional dependency is based on a candidate key

B. To allow duplicate rows in a table

C. To combine multiple tables into one

D. To remove all foreign keys from a table

Solution

1. Step 1: Understand BCNF definition

   BCNF requires that for every functional dependency X -> Y, X must be a candidate key.

2. Step 2: Analyze options

   Only To ensure every functional dependency is based on a candidate key correctly states this goal. Other options describe unrelated or incorrect concepts.

3. Final Answer:

   To ensure every functional dependency is based on a candidate key -> Option A

4. Quick Check:

   BCNF = dependencies from candidate keys [OK]

Hint: BCNF means all dependencies come from keys [OK]

Common Mistakes:

• Thinking BCNF removes foreign keys
• Confusing BCNF with merging tables
• Believing BCNF allows duplicates

2. Which of the following functional dependencies violates BCNF in a relation?

easy

A. C -> D, where C is a candidate key

B. A -> B, where A is a candidate key

C. B -> C, where B is not a candidate key

D. D -> A, where D is a candidate key

Solution

1. Step 1: Recall BCNF condition

   Every functional dependency's left side must be a candidate key.

2. Step 2: Check each dependency

   Only B -> C has a left side (B) that is not a candidate key, violating BCNF.

3. Final Answer:

   B -> C, where B is not a candidate key -> Option C

4. Quick Check:

   Dependency from non-key violates BCNF [OK]

Hint: Check if left side of dependency is a candidate key [OK]

Common Mistakes:

• Assuming all dependencies are allowed
• Confusing candidate keys with foreign keys
• Ignoring the key status of the left side

3. Consider a relation R(A, B, C) with functional dependencies: A -> B and B -> C. Which of the following is true about R?

medium

A. R is not in BCNF because B -> C violates BCNF

B. R is in BCNF because A is a candidate key

C. R is in BCNF because B determines C

D. R is not in BCNF because A -> B violates BCNF

Solution

1. Step 1: Identify candidate keys

   A determines B, and B determines C, so A determines B and C. Thus, A is a candidate key.

2. Step 2: Check BCNF condition

   Dependency B -> C has B on left, which is not a candidate key. This violates BCNF.

3. Final Answer:

   R is not in BCNF because B -> C violates BCNF -> Option A

4. Quick Check:

   Non-key dependency breaks BCNF [OK]

Hint: Check if all left sides are candidate keys [OK]

Common Mistakes:

• Assuming A -> B means all dependencies are fine
• Ignoring transitive dependencies
• Confusing BCNF with 3NF

4. Given a relation with attributes (X, Y, Z) and dependencies: X -> Y and Y -> X, what is the problem if we say this relation is in BCNF?

medium

A. There is no problem; it is in BCNF

B. X and Y are candidate keys, so BCNF is satisfied

C. X and Y together form a candidate key, so BCNF is violated

D. X and Y are not candidate keys, so BCNF is violated

Solution

1. Step 1: Analyze dependencies

   X -> Y and Y -> X mean X and Y determine each other, but neither determines Z. Candidate keys must include Z (e.g., {X, Z}, {Y, Z}).

2. Step 2: Check BCNF condition

   X -> Y has X on left, but X is not a superkey (does not determine Z), violating BCNF. Similarly for Y -> X.

3. Final Answer:

   X and Y are not candidate keys, so BCNF is violated -> Option D

4. Quick Check:

   Determinants must be superkeys covering all attributes [OK]

Hint: Mutual dependencies don't make keys without covering all attributes [OK]

Common Mistakes:

• Thinking mutual dependencies make X and Y candidate keys
• Forgetting to verify determination of all attributes like Z
• Ignoring that both sides can be keys

5. You have a relation R(A, B, C, D) with dependencies: A, B -> C, C -> D. To convert R into BCNF, what should you do?

hard

A. Remove dependency C -> D

B. Decompose R into R1(A, B, C) and R2(C, D)

C. Add C to the candidate key

D. Combine all attributes into one table

Solution

1. Step 1: Identify violating dependency

   C -> D violates BCNF because C is not a candidate key (A,B is key).

2. Step 2: Decompose relation

   Decompose into R1(A, B, C) with key (A,B) and R2(C, D) with key C to fix violation.

3. Final Answer:

   Decompose R into R1(A, B, C) and R2(C, D) -> Option B

4. Quick Check:

   Decompose on violating dependency to achieve BCNF [OK]

Hint: Decompose on dependencies with non-key left side [OK]

Common Mistakes:

• Trying to remove dependencies instead of decomposing
• Adding attributes incorrectly to keys
• Merging tables instead of decomposing