Union, intersection, difference in DBMS Theory - Step-by-Step Execution

Concept Flow - Union, intersection, difference

Start with two sets A and B

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Perform operation on A and B

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Result set is created

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Display result

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End

Start with two sets, pick an operation (union, intersection, difference), perform it, then show the result.

Execution Sample

DBMS Theory

A = {1, 2, 3}
B = {2, 3, 4}
Union = A.union(B)
Intersection = A.intersection(B)
Difference = A.difference(B)

This code shows how to find union, intersection, and difference of two sets A and B.

Analysis Table

Step	Operation	Input Sets	Process	Result
1	Union	A={1,2,3}, B={2,3,4}	Combine all unique elements from A and B	{1,2,3,4}
2	Intersection	A={1,2,3}, B={2,3,4}	Find elements common to both A and B	{2,3}
3	Difference (A-B)	A={1,2,3}, B={2,3,4}	Find elements in A not in B	{1}
4	Difference (B-A)	A={1,2,3}, B={2,3,4}	Find elements in B not in A	{4}
5	End	-	-	Operations complete

💡 All operations performed on sets A and B, results shown.

State Tracker

Variable	Start	After Union	After Intersection	After Difference (A-B)	After Difference (B-A)
A	{1,2,3}	{1,2,3}	{1,2,3}	{1,2,3}	{1,2,3}
B	{2,3,4}	{2,3,4}	{2,3,4}	{2,3,4}	{2,3,4}
Union	{}	{1,2,3,4}	{1,2,3,4}	{1,2,3,4}	{1,2,3,4}
Intersection	{}	{}	{2,3}	{2,3}	{2,3}
Difference (A-B)	{}	{}	{}	{1}	{1}
Difference (B-A)	{}	{}	{}	{}	{4}

Key Insights - 3 Insights

Why does the union include all elements from both sets without duplicates?

Union combines all unique elements from both sets, so duplicates are not repeated. See execution_table row 1 where {1,2,3,4} includes all elements from A and B.

Why is the intersection smaller or equal in size compared to the original sets?

Intersection only keeps elements present in both sets, so it can never have more elements than either set. Refer to execution_table row 2 where intersection is {2,3}.

What is the difference operation showing when we do A - B?

Difference A - B shows elements in A that are not in B. For example, {1} is in A but not in B, as shown in execution_table row 3.

Visual Quiz - 3 Questions

Look at the execution_table, what is the result of the union operation at step 1?

A {1}

B {2,3}

C {1,2,3,4}

D {4}

💡 Hint

Check the 'Result' column in execution_table row 1 for union.

At which step does the difference operation A - B produce the set {1}?

A Step 1

B Step 3

C Step 2

D Step 4

💡 Hint

Look at the 'Operation' and 'Result' columns in execution_table rows 3 and 4.

If set B changed to {3,4,5}, how would the intersection result change?

A {3}

B {4}

C {2,3}

D {}

💡 Hint

Intersection is elements common to both sets; check variable_tracker for intersection values.

Concept Snapshot

Union, Intersection, Difference of sets:
- Union (A ∪ B): all unique elements from A and B combined.
- Intersection (A ∩ B): elements common to both A and B.
- Difference (A - B): elements in A not in B.
Use these to compare or combine data sets easily.

Full Transcript

This visual execution shows how union, intersection, and difference operations work on two sets A and B. Starting with sets A={1,2,3} and B={2,3,4}, union combines all unique elements to get {1,2,3,4}. Intersection finds common elements {2,3}. Difference A-B finds elements in A not in B, which is {1}. Difference B-A finds elements in B not in A, which is {4}. The variable tracker shows how these results build step-by-step. Key moments clarify why union removes duplicates, intersection is limited to common elements, and difference shows unique elements from one set. The quiz tests understanding by asking about results at specific steps and changes if sets change.