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 βˆͺ B β€” all elements in A or B (or both)
  • Intersection: A ∩ B β€” elements in both A and B
  • Difference: A \ B β€” elements in A but not in B
  • Symmetric Difference: A Ξ” B β€” elements in A or B but not both
  • Complement: Aβ€² β€” elements in the universal set not in A

Properties

  • Commutative: A βˆͺ B = B βˆͺ A and A ∩ B = B ∩ A
  • Associative: (A βˆͺ B) βˆͺ C = A βˆͺ (B βˆͺ C)
  • Distributive: A ∩ (B βˆͺ C) = (A ∩ B) βˆͺ (A ∩ C)
  • De Morgan’s Laws: (A βˆͺ B)β€² = Aβ€² ∩ Bβ€² and (A ∩ B)β€² = Aβ€² βˆͺ Bβ€²
  • Cardinality: |A βˆͺ B| = |A| + |B| βˆ’ |A ∩ B|