<Li> (A ∩ B) ∩ C = A ∩ (B ∩ C) (\ displaystyle (A \ cap B) \ cap C = A \ cap (B \ cap C)) </Li> <Dd> Distributive laws: <Dl> <Dd> <Ul> <Li> A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (\ displaystyle A \ cup (B \ cap C) = (A \ cup B) \ cap (A \ cup C)) </Li> <Li> A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (\ displaystyle A \ cap (B \ cup C) = (A \ cap B) \ cup (A \ cap C)) </Li> </Ul> </Dd> </Dl> </Dd> <Dl> <Dd> <Ul> <Li> A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (\ displaystyle A \ cup (B \ cap C) = (A \ cup B) \ cap (A \ cup C)) </Li> <Li> A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (\ displaystyle A \ cap (B \ cup C) = (A \ cap B) \ cup (A \ cap C)) </Li> </Ul> </Dd> </Dl> <Dd> <Ul> <Li> A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) (\ displaystyle A \ cup (B \ cap C) = (A \ cup B) \ cap (A \ cup C)) </Li> <Li> A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) (\ displaystyle A \ cap (B \ cup C) = (A \ cap B) \ cup (A \ cap C)) </Li> </Ul> </Dd>

Union and intersection operations are commutative and associative operations