How do you solve the first question? Let A, B C R. We define the distance between A and B byd(A, B) = inf{|x - y| : x E A, y E B}.Show that if A is compact and B is closed, and d(A, B) = 0, then ANB#Ø.• Give examples of d(A, B) = 0, ANB=Ø wheno A and Bare merely closed;o A and Bare open and bounded.

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Answered: • Show that if A is compact and Bis…

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• Show that if A is compact and Bis closed, and d(A, B) = 0, then ANB÷Ø.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.1: Sets And Geometry

Problem 7E: Let A, B, and C lie on a straight line as shown near Exercise 8. Classify these claims as true or...

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Question

How do you solve the first question?

Let A, B C R. We define the distance between A and B by
d(A, B) = inf{|x - y| : x E A, y E B}.
Show that if A is compact and B is closed, and d(A, B) = 0, then ANB#Ø.
• Give examples of d(A, B) = 0, ANB=Ø when
o A and Bare merely closed;
o A and Bare open and bounded.

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