Set operations combine or compare collections: Union (A∪B) = all elements in either set. Intersection (A∩B) = elements in both. Difference (A−B) = in A but not B. Symmetric difference (A△B) = in one but not both. These operations are fundamental to databases (SQL JOINs), probability, and logic.
How to Use
Enter two sets:
- Set A: Comma-separated values
- Set B: Comma-separated values
- Operations: All computed automatically
Operations
- A∪B: elements in A OR B (or both)
- A∩B: elements in A AND B
- A−B: elements in A but NOT B
- A△B: elements in exactly one set
Properties
- |A∪B| = |A| + |B| − |A∩B|
- A∪B = B∪A (commutative)
- A∩B = B∩A (commutative)
- A−B ≠ B−A (not commutative)
Step-by-Step Instructions
- 1Enter Set A elements.
- 2Enter Set B elements.
- 3View all operations.
- 4Check cardinalities.
- 5Test subset relationships.