Closure of attributes in DBMS Theory - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to find the closure of attribute set A under functional dependencies F.

DBMS Theory

SELECT closure FROM attribute_closure WHERE attributes = '[1]';

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

AA+

BA

Cclosure

DF

Attempts:

3 left

💡 Hint

Common Mistakes

Using just 'A' instead of 'A+' for closure notation.

Confusing the closure with the set of functional dependencies.

The closure of attribute set A is denoted as A+ and includes all attributes functionally determined by A under F.

2fill in blank

medium

Complete the code to check if attribute B is in the closure of attribute set A.

DBMS Theory

IF '[1]' IN closure_of_A THEN RETURN TRUE ELSE RETURN FALSE;

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

AC

BB

CA

DF

Attempts:

3 left

💡 Hint

Common Mistakes

Checking for attribute A instead of B.

Using the set of dependencies F instead of an attribute.

We check if attribute B is in the closure of A to determine if A functionally determines B.

3fill in blank

hard

Fix the error in the code to compute the closure of attribute set X under F.

DBMS Theory

closure = [1](X, F)

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

Acompute_closure

Bclosure_compute

Cclosure

Dcompute

Attempts:

3 left

💡 Hint

Common Mistakes

Using incomplete or incorrect function names.

Using variable names instead of function names.

The standard function name to compute closure is often 'compute_closure'.

4fill in blank

hard

Fill both blanks to complete the code that computes closure of attributes in set S under dependencies D.

DBMS Theory

closure = [1]([2], D)

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

Acompute_closure

BS

CX

DF

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping the function name and attribute set.

Using incorrect variable names.

The function to compute closure is 'compute_closure' and the attribute set is 'S'.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each attribute in attrs to its closure under F.

DBMS Theory

closures = [1]: [2](attr, [3]) for attr in attrs

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Aattr

Bcompute_closure

CF

Dclosure

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong keys or values in the dictionary comprehension.

Confusing the function name or dependency set.

This comprehension creates a dictionary where each key is an attribute and the value is its closure computed by 'compute_closure' under dependencies F.

Practice

1. What does the closure of attributes represent in database design?

easy

A. The total number of tables in a database

B. All attributes functionally determined by a given set of attributes

C. The list of all primary keys in a database

D. The count of foreign keys referencing a table

Solution

1. Step 1: Understand the concept of closure

   The closure of a set of attributes includes all attributes that can be functionally determined from it using given dependencies.

2. Step 2: Relate closure to database design

   This helps identify all attributes dependent on a set, useful for normalization and design.

3. Final Answer:

   All attributes functionally determined by a given set of attributes -> Option B

4. Quick Check:

   Closure = all functionally determined attributes [OK]

Hint: Closure means all attributes you can find from given ones [OK]

Common Mistakes:

• Confusing closure with number of tables
• Thinking closure lists keys only
• Mixing closure with foreign key counts

2. Which of the following is the correct notation for the closure of attribute set A given functional dependencies F?

easy

A. A+

B. F+

C. A*

D. F*

Solution

1. Step 1: Recall standard notation

   The closure of an attribute set A under functional dependencies F is denoted as A+.

2. Step 2: Differentiate from other notations

   F+ denotes closure of the set of functional dependencies, not attributes. A* and F* are not standard notations here.

3. Final Answer:

   A+ -> Option A

4. Quick Check:

   Attribute closure = A+ notation [OK]

Hint: Closure of attributes is always written as A+ [OK]

Common Mistakes:

• Using F+ for attribute closure
• Confusing closure notation with star (*)
• Mixing attribute and dependency closures

3. Given attributes A, B, C, D and functional dependencies:
A -> B, B -> C, C -> D. What is the closure of {A}?

medium

A. {A, B, C, D}

B. {A, B, C}

C. {A, B}

D. {A, D}

Solution

1. Step 1: Start with initial set {A}

   Closure begins with {A}.

2. Step 2: Apply functional dependencies repeatedly

   From A -> B, add B; from B -> C, add C; from C -> D, add D.

3. Final Answer:

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

4. Quick Check:

   Applying all dependencies gives full set [OK]

Hint: Keep adding attributes until no new ones appear [OK]

Common Mistakes:

• Stopping after first dependency
• Forgetting to add transitive dependencies
• Confusing closure with just initial attributes

4. Identify the error in this closure calculation: Given A -> B, B -> C, and starting with {A}, the closure is calculated as {A, C}.

medium

A. Closure should be empty

B. Incorrect initial attribute set

C. Wrong functional dependencies used

D. Missed adding attribute B before C

Solution

1. Step 1: Check closure calculation steps

   Starting with {A}, applying A -> B adds B first.

2. Step 2: Verify transitive dependencies

   Only after B is added can B -> C add C. Skipping B is incorrect.

3. Final Answer:

   Missed adding attribute B before C -> Option D

4. Quick Check:

   Closure must add intermediate attributes [OK]

Hint: Add attributes step-by-step, don't skip intermediates [OK]

Common Mistakes:

• Skipping intermediate attributes
• Assuming direct jump to last attribute
• Ignoring order of dependencies

5. Given attributes A, B, C, D, E and functional dependencies:
A -> BC, CD -> E, B -> D. What is the closure of {A, D}?

hard

A. {A, C, D, E}

B. {A, B, C, D}

C. {A, B, C, D, E}

D. {A, B, C, E}

Solution

1. Step 1: Start with {A, D}

   Initial closure is {A, D}.

2. Step 2: Apply A -> BC

   Add B and C, closure becomes {A, B, C, D}.

3. Step 3: Apply B -> D

   D already included, no change.

4. Step 4: Apply CD -> E

   Since C and D are in closure, add E.

5. Final Answer:

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

6. Quick Check:

   All attributes reachable from {A, D} included [OK]

Hint: Use all dependencies repeatedly until no new attributes [OK]

Common Mistakes:

• Not applying CD -> E after adding C
• Forgetting to add B and C from A
• Stopping closure too early