Venn Diagram Maker
Visualize set union, intersection, difference, symmetric difference, and complement. Enter set elements and drag circles to reposition.
Set Operations
Drag circle centers to reposition
Properties
| Set A | -- |
| Set B | -- |
| |A| | -- |
| |B| | -- |
| Operation | -- |
| Result | -- |
| |Result| | -- |
The Math Behind It
Set Operations
- Union: A ∪ B — all elements in A or B (or both)
- Intersection: A ∩ B — elements in both A and B
- Difference: A \ B — elements in A but not in B
- Symmetric Difference: A Δ B — elements in A or B but not both
- Complement: A′ — elements in the universal set not in A
Properties
- Commutative: A ∪ B = B ∪ A and 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′ and (A ∩ B)′ = A′ ∪ B′
- Cardinality: |A ∪ B| = |A| + |B| − |A ∩ B|
You're crushing it!