Kümelerde işlemlerin özellikleri:
- A ∪ A = A
- A ∩ A = A
- A ∪ B = B ∪ A
- A ∩ B = B ∩ A
- A ∪ Ø = A
- A ∩ Ø = Ø
- A ∪ E = E
- A ∩ E = A
- A ∪ A′ = E
- A ∩ A′ = Ø
- E′ = Ø
- Ø′ = E
- (A′)′ = A
- A′ = E – A
- A ∪ (B ∪ C) = (A ∪ B) ∪ C
- A ∩ (B ∩ C) = (A ∩ B) ∩ C
- A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
- A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
- s(A ∪ B) = s(A) + s(B) – s(A ∩ B)
- s(A∪B ∪ C) = s(A) + s(B) + s(C) – s(A ∩ B)– s(A ∩ C) – s(B ∩ C) + s(A ∩ B ∩ C)
- A – B = A ∩ B′
- A ⊂ B ⇒ B′ ⊂ A′
- A ⊂ B ⇒ A ∪ B = B
- A ⊂ B ⇒ A ∩ B = A
