Set algebra (union, intersection, difference) in Swift - Step-by-Step Execution

Concept Flow - Set algebra (union, intersection, difference)

Start with two sets A and B

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Choose operation

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Union

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Combine all

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Result set

We start with two sets and pick an operation: union combines all elements, intersection finds common elements, and difference finds elements in the first set not in the second.

Execution Sample

Swift

let A: Set = [1, 2, 3, 4]
let B: Set = [3, 4, 5, 6]

let unionSet = A.union(B)
let intersectionSet = A.intersection(B)
let differenceSet = A.subtracting(B)

This code creates two sets A and B, then finds their union, intersection, and difference.

Execution Table

Step	Operation	Sets Involved	Result	Explanation
1	Define A	A = {1, 2, 3, 4}	{1, 2, 3, 4}	Set A is created with elements 1,2,3,4
2	Define B	B = {3, 4, 5, 6}	{3, 4, 5, 6}	Set B is created with elements 3,4,5,6
3	Union	A ∪ B	{1, 2, 3, 4, 5, 6}	All unique elements from A and B combined
4	Intersection	A ∩ B	{3, 4}	Only elements common to both A and B
5	Difference	A - B	{1, 2}	Elements in A that are not in B
6	End	-	-	All operations complete

💡 All set operations performed; execution ends.

Variable Tracker

Variable	Start	After Union	After Intersection	After Difference	Final
A	{1, 2, 3, 4}	{1, 2, 3, 4}	{1, 2, 3, 4}	{1, 2, 3, 4}	{1, 2, 3, 4}
B	{3, 4, 5, 6}	{3, 4, 5, 6}	{3, 4, 5, 6}	{3, 4, 5, 6}	{3, 4, 5, 6}
unionSet	-	{1, 2, 3, 4, 5, 6}	{1, 2, 3, 4, 5, 6}	{1, 2, 3, 4, 5, 6}	{1, 2, 3, 4, 5, 6}
intersectionSet	-	-	{3, 4}	{3, 4}	{3, 4}
differenceSet	-	-	-	{1, 2}	{1, 2}

Key Moments - 3 Insights

Why does the union set contain no duplicates even though 3 and 4 appear in both sets?

Because sets automatically store unique elements, the union combines all elements but keeps only one copy of duplicates, as shown in step 3 of the execution table.

Why is the difference set only {1, 2} and not including 3 or 4?

Difference means elements in A that are not in B. Since 3 and 4 are in both sets, they are excluded. This is clear in step 5 of the execution table.

Does the intersection set change the original sets A or B?

No, intersection creates a new set with common elements but does not modify A or B, as shown in the variable tracker where A and B remain unchanged.

Visual Quiz - 3 Questions

Look at the execution table at step 4. What elements are in the intersection set?

A {1, 2}

B {3, 4}

C {5, 6}

D {1, 2, 3, 4, 5, 6}

💡 Hint

Check the 'Result' column at step 4 in the execution table.

At which step does the difference operation occur?

A Step 5

B Step 4

C Step 3

D Step 6

💡 Hint

Look for the row labeled 'Difference' in the 'Operation' column.

If set B was changed to {2, 3, 4}, what would be the difference set after step 5?

A {1, 2}

B {1, 2, 3}

C {1}

D {}

💡 Hint

Difference is elements in A not in B; check variable_tracker logic.

Concept Snapshot

Set algebra in Swift:
- union: A.union(B) combines all unique elements
- intersection: A.intersection(B) finds common elements
- difference: A.subtracting(B) finds elements in A not in B
Sets store unique values only
Operations return new sets, originals unchanged

Full Transcript

This visual execution shows how to perform set algebra operations in Swift. We start with two sets A and B. We then perform union to combine all unique elements, intersection to find common elements, and difference to find elements in A not in B. Each step is shown with the sets involved and the results. Variables are tracked to show no original sets change. Key moments clarify common confusions about duplicates, difference meaning, and immutability. The quiz tests understanding of the execution steps and results.