Let A, B, and C be three events on a sample space . Examine, possibly with the

Let A, B, and C be three events on a sample space Ω. Examine, possibly with the aid of Venn diagrams, which of the following results are always true:

(i) (A − AB)B = AB;

(ii) (A ∪ B)′C = A′B′C;

(iii) (AB)′C′ = (ABC)′;

(iv) AB ⊆ A ⊆ A ∪ B ∪ C;

(v) A′B ∪ C′B = (A ∪ C)′B;

(vi) (A − B) − C = A − (B − C).