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Prove that if A₁, A2, ..., An are any n ≥ 2 sets, then A₁ A₂ An A₂ = A₁ UA₂ U... U An.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Prove the following question by induction:

(Please elaborate as much as possible step by step on how to solve this question, I understand Induction but I have no idea how to do it on sets)

Prove that if A1, A2, ..., An are any n ≥ 2 sets, then
A₁
A₂
A₂ = A₁ UA₂ U... U An.
n

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