(b) Is the converse valid? Give a proof or counterexample. #7. (a) Suppose U and V are open subsets of R". Prove that U U V and UnV are open as well. (Recall that UUV= {x e R2 xe U or x e V} and Un V = {x e R" : x e U and x e V}.) (b) Suppose C and D are closed subsets of R". Prove that C UD and CnD are closed as well. 8. Let S C R". We say a e S is an interior point of S if some neighborhood of a is contained in S.
(b) Is the converse valid? Give a proof or counterexample. #7. (a) Suppose U and V are open subsets of R". Prove that U U V and UnV are open as well. (Recall that UUV= {x e R2 xe U or x e V} and Un V = {x e R" : x e U and x e V}.) (b) Suppose C and D are closed subsets of R". Prove that C UD and CnD are closed as well. 8. Let S C R". We say a e S is an interior point of S if some neighborhood of a is contained in S.
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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I need help for number 7. Thanks!
![(b) Is the converse valid? Give a proof or counterexample.
#7. (a) Suppose U and V are open subsets of R". Prove that U U V and UnV are open as well.
(Recall that UUV= {x e R2 xe U or x e V} and Un V = {x e R" : x e U and x e V}.)
(b) Suppose C and D are closed subsets of R". Prove that C UD and CnD are closed as well.
8. Let S C R". We say a e S is an interior point of S if some neighborhood of a is contained in S.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1a3b0a85-5819-488a-b640-64960995ba98%2F87966b05-323e-4df1-b8b5-d90cd7e6a06a%2Ffuuyonk.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Is the converse valid? Give a proof or counterexample.
#7. (a) Suppose U and V are open subsets of R". Prove that U U V and UnV are open as well.
(Recall that UUV= {x e R2 xe U or x e V} and Un V = {x e R" : x e U and x e V}.)
(b) Suppose C and D are closed subsets of R". Prove that C UD and CnD are closed as well.
8. Let S C R". We say a e S is an interior point of S if some neighborhood of a is contained in S.
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