Let A, B, and C be any three events defined on a sample space S. Show that

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Let A, B, and C be any three events defined on a sample space S. Show that
(a) The outcomes in A ∪ (B ∩ C) are the same as the outcomes in (A ∪ B) ∩ (A ∪C).
(b) The outcomes in A ∩ (B ∪ C) are the same as the outcomes in (A ∩ B) ∪ (A ∩C).
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