Prove Theorem 2.12 by making use of the following generalization of the distributive law given in part

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Prove Theorem 2.12 by making use of the following generalization of the distributive law given in part (b) of Exercise 2.1: A ∩(B1. B2. · · · ∪ Bk) =(A ∩ B1) .(A ∩ B2) ∪ · · · ∪ (A ∩ Bk)
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