Question: In the statements below A, B, C, and D are events. Find those statements or formulas that are true. (i) If A B =

In the statements below A, B, C, and D are events. Find those statements or formulas that are true. (i) If A ∩ B = A ∩ C, then B = C. (ii) A ∪ (A ∩ B) ∪ (A ∩ Bc) = A.

(iii) A ∪ (A ∩ B) ∪ (A ∩ Bc) = B. (iv) If A\B = C, then A = B ∪ C. (v) (A ∪ B) ∩

(C ∪ D)=(A ∩ C) ∪ (A ∩ D) ∪ (B ∩ C) ∪ (B ∩ D). (vi)(A ∩ B) ∪ (C ∩ D)=(A ∪

C) ∩ (A ∪ D) ∩ (B ∪ C) ∩ (B ∪ D). (vii) (Ac ∪ Bc ∪ Cc)c = Ac ∩ Bc ∩ Cc. (viii) If A ⊂ B, and B ∩ C = ∅, then Cc ∩ A ∩ Bc = ∅. (ix) If A ∩ B, A ∩ C and B ∩ C are not empty, then A ∩ B ∩ C is not empty. (x) Show that (A ÷ B) ÷ C = A ÷ (B ÷ C).

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