Crisp sets demonstrate certain properties, as follows:
- Commutivity:
- A ∪ B = B ∪ A
- A ∩ B = B ∩ A
- Associativity:
- A ∪ (B ∪ C) = (A ∪ B) ∪ C
- A ∩ (B ∩ C) = (A ∩ B) ∩ C
- Distributivity:
- A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
- A ∩ (A ∪ C) = (A ∩ B) ∪ (A ∩ C)
- Idempotency:
- A ∪ A = A
- A ∩ A = A
- Transitivity:
- If A ⊆ B ⊆ C then A ⊆ C