Please prove the following and write the proof step by step with explanation, thank you in advance Consider the indexed collection (AnneN of sets given byfor every natural number n.d.An = {x € Z : |x| < 42 +n and x < 42/n}e.Show that Unen An = {x € Z: x ≤ 41}.Prove that the sets An are pairwise distinct, i.e. if m, n are natural numberswith m‡n, then Am ‡ An.

d. To show that , need to prove two inclusions:1. :Let be an element in . This means belongs to at…

Answered: Consider the indexed collection {An)neN…

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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A clothing company must deliver an order within 12 days. In order to fulfill the order, he must manufacture 2,000 garments daily. However, it suffers a breakdown that stops production for two (2) days. How many garments will you have to make daily to face this new situation? Write an opening contribution indicating why you used direct or indirect variation. Justify your answer with arguments. Add the math ecuation
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Consider the indexed collection {An)neN of sets given by for every natural number n. d. An = {x € Z : |x| < 42 +n and x < 42/n} e. Show that Unen An = {x € Z :x≤ 41}. nEN Prove that the sets An are pairwise distinct, i.e. if m, n are natural numbers with m‡n, then Am ‡ An.