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Let{Ai :i∈I} be a collection of sets indexed by a set I. (a) Prove that if...

  1. Let{Ai :i∈I} be a collection of sets indexed by a set I.
    (a) Prove that if there exists i0 ∈ I such that Ai ⊆ Ai0 for all i ∈ I, then ∪i∈I Ai = Ai0.

  2. (b) Prove that if there exists i0 ∈ I such that Ai0 ⊆ Ai for all i ∈ I, then ∩i∈I Ai = Ai0.

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