) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.
) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.
Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
How do you prove (b)?
Note that the symbol ° represents the interior of a set
![Let A and Bdenote subsets of R".
(a) Prove that ANBCAN B. Give an example to show that equality does not always hold.
(b) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.
(c) Give an example of a function that is C2 but not C³.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc15f731f-0363-4c98-a248-c9121c1de30f%2F144d9fb0-af26-4e19-b07c-88ecefb20690%2Fb1203eu_processed.png&w=3840&q=75)
Transcribed Image Text:Let A and Bdenote subsets of R".
(a) Prove that ANBCAN B. Give an example to show that equality does not always hold.
(b) Prove that A° U B° C (AU B)°. Give an example to show that equality does not always hold.
(c) Give an example of a function that is C2 but not C³.
![1. There is some magnification beyond which you see only points that belong to S. More
precisely,
3e > 0: B(x; e) C S.
(1)
Def. 4 (Interior)
In this case, we say that x belongs to the interior of S. We write Sint for the set of all
such points.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc15f731f-0363-4c98-a248-c9121c1de30f%2F144d9fb0-af26-4e19-b07c-88ecefb20690%2Fzigais_processed.png&w=3840&q=75)
Transcribed Image Text:1. There is some magnification beyond which you see only points that belong to S. More
precisely,
3e > 0: B(x; e) C S.
(1)
Def. 4 (Interior)
In this case, we say that x belongs to the interior of S. We write Sint for the set of all
such points.
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