Candidate key finding using closure in DBMS Theory - Step-by-Step Execution

Concept Flow - Candidate key finding using closure

Start with attribute set S

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Compute closure S+ using FDs

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Check if S+ contains all attributes

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Candidate key

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End

Start with a set of attributes, find its closure using functional dependencies, check if closure covers all attributes to identify candidate keys.

Execution Sample

DBMS Theory

Attributes: {A,B,C,D}
FDs: A->B, B->C, C->D
Check closure of {A}

Find closure of attribute set {A} to see if it covers all attributes, indicating a candidate key.

Analysis Table

Step	Current Closure	FD Applied	New Attributes Added	Closure After Step
1	{A}	A->B	B	{A,B}
2	{A,B}	B->C	C	{A,B,C}
3	{A,B,C}	C->D	D	{A,B,C,D}
4	{A,B,C,D}	No more FDs	None	{A,B,C,D}

💡 Closure contains all attributes {A,B,C,D}, so {A} is a candidate key.

State Tracker

Variable	Start	After 1	After 2	After 3	Final
Closure	{A}	{A,B}	{A,B,C}	{A,B,C,D}	{A,B,C,D}

Key Insights - 2 Insights

Why do we add new attributes to the closure only when the left side of an FD is in the closure?

Because only when the FD's left side attributes are in the closure can we infer the right side attributes, as shown in steps 1-3 of the execution_table.

What if the closure does not contain all attributes after applying all FDs?

Then the attribute set is not a candidate key; we must try a different set, as indicated by the 'No' branch in the concept_flow.

Visual Quiz - 3 Questions

Look at the execution_table, what is the closure after step 2?

A {A,B}

B {A,B,C}

C {A,B,C,D}

D {A}

💡 Hint

Check the 'Closure After Step' column for step 2 in the execution_table.

At which step does the closure first include attribute D?

A Step 1

B Step 2

C Step 3

D Step 4

💡 Hint

Look at the 'New Attributes Added' column to see when D is added.

If the FD C->D was missing, what would be the final closure of {A}?

A {A,B,C}

B {A,B}

C {A,B,C,D}

D {A}

💡 Hint

Consider the closure steps without applying C->D from the execution_table.

Concept Snapshot

Candidate key finding using closure:
- Start with attribute set S
- Compute closure S+ by applying FDs repeatedly
- If S+ contains all attributes, S is a candidate key
- Otherwise, try different attribute sets
- Closure helps find minimal keys covering all attributes

Full Transcript

To find candidate keys using closure, start with a set of attributes. Compute its closure by adding attributes that can be functionally determined using the given functional dependencies. Repeat until no new attributes can be added. If the closure contains all attributes of the relation, the starting set is a candidate key. If not, try another set. For example, with attributes A,B,C,D and FDs A->B, B->C, C->D, the closure of {A} is computed stepwise adding B, then C, then D, resulting in {A,B,C,D}. Since this closure contains all attributes, {A} is a candidate key.