Suppose that {A_n}[n=1 to ∞] is a pairwise disjoint sequence of nonempty subsets
of Ω whose union is Ω.

(a) Prove that the collection D of countable (including empty) unions of members of
　　 {A_n}[n=1 to ∞] is a σ-algebra.

(b) Prove that the collection E of finite (including empty) unions of members of
　　 {A_n}[n=1 to ∞] is not an algebra and, hence, not a σ-algebra.

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