Set Theory
Understanding sets, set operations, and set theory fundamentals
Interactive Set Theory Visualization
Welcome to the Set Theory Explorer
This interactive visualization helps you understand set theory concepts including set operations, Venn diagrams, and set notation. Explore how different operations combine sets.
What you can explore:
- Union (A ∪ B) - All elements in A or B
- Intersection (A ∩ B) - Elements in both A and B
- Complement (A') - Elements not in A
- Difference (A - B) - Elements in A but not in B
- Symmetric Difference (A Δ B) - Elements in A or B but not both
How to Use This Visualization
Interactive Features:
- • Enter Sets - Input elements for sets A, B, and universal set
- • Select Operation - Choose from 5 set operations
- • Toggle Highlight - Show/hide operation result
- • View Elements - See elements in each region
What You'll See:
- • Venn Diagram - Visual representation of sets
- • Set A (green circle) - First set
- • Set B (blue circle) - Second set
- • Operation Result (amber highlight) - Result of selected operation
5 elements
5 elements
10 elements
All elements in A or B or both
Operation Result: A ∪ B
Result Set: A ∪ B
{1, 2, 3, 4, 5, 6, 7, 8}
8 elements
All elements in A or B or both
Set Information
Set A
{1, 2, 3, 4, 5}
|A| = 5
Set B
{4, 5, 6, 7, 8}
|B| = 5
A ∩ B
{4, 5}
|A ∩ B| = 2
Set Operations
Union (A ∪ B): All elements that are in A or B or both. A ∪ B = 1, 2, 3, 4, 5, 6, 7, 8
Intersection (A ∩ B): Elements that are in both A and B. A ∩ B = 4, 5
Complement (A'): All elements in universal set U that are not in A. A' = U - A
Difference (A - B): Elements in A but not in B. A - B = 1, 2, 3
Symmetric Difference (A Δ B): Elements in A or B but not in both. A Δ B = (A - B) ∪ (B - A)
Set Theory Properties
Commutative: A ∪ B = B ∪ A, A ∩ B = B ∩ A
Associative: (A ∪ B) ∪ C = A ∪ (B ∪ C)
Distributive: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
De Morgan's Laws: (A ∪ B)' = A' ∩ B', (A ∩ B)' = A' ∪ B'
Cardinality: |A ∪ B| = |A| + |B| - |A ∩ B|
Lessons
Individual learning units
Lessons coming soon