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