Question: For any events A, B, and C in a sample space, verify the truth of the following relations: (i) (A B) C =

For any events A, B, and C in a sample space, verify the truth of the following relations:

(i) (A − B) − C = (A − C) − (B − C);

(ii) (B − A) ∪ (C − A) = (B ∪ C) − A;

(iii) A − (B − C) = (A − B) ∪ (AC);

(iv) (A − B) ∪ B = A ∪ B;
(v) A(B − C) = AB − AC;
(vi) A ∪ B ∪ C = (A − B) ∪ (B − C) ∪ (C − A) ∪ (ABC).

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