Union and intersection in Python - Step-by-Step Execution

Concept Flow - Union and intersection

Start with two sets

↓

Find Union: all unique elements

↓

Find Intersection: common elements

↓

Output both results

↓

End

We start with two sets, then find their union (all unique items) and intersection (items both sets share), and finally output the results.

Execution Sample

Python

set1 = {1, 2, 3}
set2 = {2, 3, 4}
union = set1 | set2
intersection = set1 & set2
print(union)
print(intersection)

This code finds the union and intersection of two sets and prints them.

Execution Table

Step	Action	Expression	Result
1	Define set1	set1 = {1, 2, 3}	{1, 2, 3}
2	Define set2	set2 = {2, 3, 4}	{2, 3, 4}
3	Calculate union	union = set1 | set2	{1, 2, 3, 4}
4	Calculate intersection	intersection = set1 & set2	{2, 3}
5	Print union	print(union)	{1, 2, 3, 4} (order may vary)
6	Print intersection	print(intersection)	{2, 3} (order may vary)

💡 All steps completed, union and intersection printed.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
set1	undefined	{1, 2, 3}	{1, 2, 3}	{1, 2, 3}	{1, 2, 3}	{1, 2, 3}
set2	undefined	undefined	{2, 3, 4}	{2, 3, 4}	{2, 3, 4}	{2, 3, 4}
union	undefined	undefined	undefined	{1, 2, 3, 4}	{1, 2, 3, 4}	{1, 2, 3, 4}
intersection	undefined	undefined	undefined	undefined	{2, 3}	{2, 3}

Key Moments - 3 Insights

Why does the union use the | operator instead of +?

The | operator combines all unique elements from both sets without duplicates, while + is not defined for sets and would cause an error. See execution_table step 3.

Why does the intersection use the & operator?

The & operator finds only elements present in both sets, which is the definition of intersection. See execution_table step 4.

Why might the printed order of elements vary?

Sets do not keep order, so when printed, elements can appear in any order. This is normal and expected. See execution_table steps 5 and 6.

Visual Quiz - 3 Questions

Look at the execution_table, what is the value of 'union' after step 3?

A {1, 2, 3, 4}

B {2, 3}

C {1, 2, 3}

D undefined

💡 Hint

Check the 'Result' column in execution_table row with Step 3.

At which step is the intersection calculated?

A Step 2

B Step 3

C Step 4

D Step 5

💡 Hint

Look for the action 'Calculate intersection' in execution_table.

If set2 was {3, 4, 5} instead, what would be the intersection after step 4?

A {2, 3}

B {3}

C {1, 2, 3, 4, 5}

D {}

💡 Hint

Intersection is elements common to both sets; check variable_tracker logic.

Concept Snapshot

Union and Intersection of sets in Python:
- Use | for union (all unique elements)
- Use & for intersection (common elements)
- Sets are unordered collections
- Printing sets may show elements in any order
- Useful for combining or comparing groups

Full Transcript

This visual execution shows how to find the union and intersection of two sets in Python. We start by defining two sets, set1 and set2. Then we calculate the union using the | operator, which combines all unique elements from both sets. Next, we calculate the intersection using the & operator, which finds elements present in both sets. Finally, we print both results. The execution table traces each step and the variable tracker shows how variables change. Key moments clarify why we use | and & operators and why set order is not guaranteed. The quiz tests understanding of these steps and outcomes.

Practice

1. What does the union operation do when applied to two sets in Python?

easy

A. Combines all unique elements from both sets

B. Finds elements only in the first set

C. Finds elements only in the second set

D. Finds elements common to both sets

Solution

1. Step 1: Understand union operation

   The union of two sets includes every unique element from both sets without duplicates.

2. Step 2: Compare with other options

   Options B and C describe subsets, and D describes intersection, not union.

3. Final Answer:

   Combines all unique elements from both sets -> Option A

4. Quick Check:

   Union = all unique elements combined [OK]

Hint: Union joins all unique items from both sets [OK]

Common Mistakes:

• Confusing union with intersection
• Thinking union only takes elements from one set
• Assuming union keeps duplicates

2. Which of the following is the correct syntax to find the intersection of two sets a and b in Python?

easy

A. a + b

B. a | b

C. a & b

D. a - b

Solution

1. Step 1: Recall intersection syntax

   In Python, the intersection of two sets is found using the & operator or the .intersection() method.

2. Step 2: Check other operators

   | is union, + is invalid for sets, - is difference.

3. Final Answer:

   a & b -> Option C

4. Quick Check:

   Intersection uses & operator [OK]

Hint: Use & for intersection of sets [OK]

Common Mistakes:

• Using | instead of & for intersection
• Trying to add sets with + operator
• Confusing difference (-) with intersection

3. What is the output of the following code?

set1 = {1, 2, 3, 4}
set2 = {3, 4, 5, 6}
print(set1.intersection(set2))

medium

A. {1, 2}

B. {5, 6}

C. {1, 2, 3, 4, 5, 6}

D. {3, 4}

Solution

1. Step 1: Identify intersection elements

   The intersection contains elements present in both sets: {3, 4}.

2. Step 2: Confirm output

   Printing the intersection returns {3, 4} exactly.

3. Final Answer:

   {3, 4} -> Option D

4. Quick Check:

   Common elements = {3, 4} [OK]

Hint: Intersection shows only common elements [OK]

Common Mistakes:

• Confusing union with intersection output
• Expecting all elements combined
• Mixing up set contents

4. The following code is intended to print the union of two sets, but it causes an error. What is the problem?

set1 = {1, 2, 3}
set2 = {3, 4, 5}
print(set1 + set2)

medium

A. Sets cannot be added with + operator

B. The sets are empty

C. The print statement is missing parentheses

D. The sets have overlapping elements

Solution

1. Step 1: Identify the error cause

   Python sets do not support the + operator; this causes a TypeError.

2. Step 2: Correct way to union sets

   Use | operator or .union() method to combine sets.

3. Final Answer:

   Sets cannot be added with + operator -> Option A

4. Quick Check:

   + operator invalid for sets [OK]

Hint: Use | or .union(), not + for sets [OK]

Common Mistakes:

• Trying to add sets with +
• Ignoring error message
• Confusing list addition with set union

5. Given two lists of student names, list1 = ['Anna', 'Bob', 'Cara'] and list2 = ['Bob', 'Diana', 'Anna'], which Python code correctly finds students present in both lists using set operations?

hard

A. list1 | list2

B. set(list1) & set(list2)

C. set(list1) + set(list2)

D. list1.intersection(list2)

Solution

1. Step 1: Convert lists to sets for set operations

   Lists must be converted to sets to use intersection (&) operator.

2. Step 2: Use & operator to find common elements

   set(list1) & set(list2) returns elements in both sets.

3. Step 3: Check other options

   list1 | list2 uses | on lists (invalid), C uses + on sets (invalid), D calls intersection on list (no such method).

4. Final Answer:

   set(list1) & set(list2) -> Option B

5. Quick Check:

   Convert lists to sets, then & for intersection [OK]

Hint: Convert lists to sets before intersection [OK]

Common Mistakes:

• Using + or | on lists directly
• Calling set methods on lists
• Not converting lists to sets first