Let A1, A2, . . . , An be sets. Prove that for every integer n ≥ 1, we have: (A1 ∪ A2 ∪ ··· ∪ An)c = A1c ∩ A2c ∩ ··· ∩ Anc. (Using mathematic induction)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 3E
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Let A1, A2, . . . , An be sets. Prove that for every integer n ≥ 1, we have:
(A1 ∪ A2 ∪ ··· ∪ An)c = A1c ∩ A2c ∩ ··· ∩ Anc. (Using mathematic induction)

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