Mark all true statements (there might be more than one statement that is true).O Every finite subset AC R is closed.O A= {1} is relatively open in X=[-1,2].O A=(x² - 1:x € (-1,1) } is closed in R.Let A be countable subset of R. Then A is closed.The set A=A=n: nENU {0} is closed.ENJU 10

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Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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2. Prove tne Follow Statements: (i) The infimum of a set S ip it exist ,lt is unique. 11) Let AC IK be a non-empty Subset of positive real numbers which is bounded above and let r70. Detine the following Subset of IR. B = Cr+a: aCAY and C=[ra : a6 AJ Prove that If Sup(A)=u, then Sup(B) =rtu and Sup (c) =ru.
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Let f {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} → {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be defined by f(x) = 2x if x 6. Select all the elements of f({5,6}). 01 3 2 4 Select all the elements of f-¹({5,6}). 3 04 Select all the elements of ƒ−¹(ƒ({5,6})). 3 04 2 Select all the elements of ƒ(ƒ¯¹({5,6})). 01 3 04 5 5 06 6 07 07 07 07 U O 8 8 8 8 9 9 9 ✔10 10 10 10
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atements (there might be more tha O Every finite subset AC R is closed. O A={1} is relatively open in X=[-1,2]. O A={x²-1:xE (-1,1) } is closed in R. Let A be countable subset of R. Then A is c The set A= n : nENU {0} is closed. ENJU!