LAW OF SET THEORY

1. COMMUTATIVE LAW

1.1. •(A ∪ B) = (B ∪ A) •(A ∩ B) = (B ∩ A)

2. ASSOCIATIVE LAW

2.1. •(A ∪ B) ∪ C = A ∪ (B ∪ C) •(A ∩ B) ∩ C = A ∩ (B ∩ C)

3. DISTRIBUTIVE LAW

3.1. •A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) •A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ B)

4. INVERSE LAW

4.1. •A ∪ A' = ξ •A ∩ A' = Ф

5. DOMINATIVE LAW

5.1. •A ∪ ξ = ξ •A ∩ Ф = Ф

6. DEFINITION OF SUBSTRACTION

6.1. •A - B = A\B = A ∩ B'

7. DOUBLE COMPLEMENT LAW

7.1. A'' = A

8. DEMORGAN'S LAW

8.1. •(A ∩ B)' = A' ∪ B' •(A ∪ B) = (B ∪ A)

9. IDEMPOTENT LAW

9.1. •A ∩ A = A •A ∪ A = A

10. IDENTITY LAW

10.1. •A ∩ ξ = A •A ∪ Ф = A

11. ABSORPTION LAW

11.1. •A ∪ (A ∩ B) = A •A ∩ (A ∪ B) = A