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Ex: Let (X, d) be a metric space and E, andE2 EX Show that whether each one of the following statement true or false or not and why. 1. Int(E, U E2) = Int(E,) U Int(E2) 2. Int(E, n E2) = Int(E1) n Int(E2) 3. Int(E, – E2) = Int(E,) – Int(E2) %3D %3D %3D

Ex: Let (X, d) be a metric space and E, andE2 EX Show that whether each one of the following statement true or false or not and why. 1. Int(E, U E2) = Int(E,) U Int(E2) 2. Int(E, n E2) = Int(E1) n Int(E2) 3. Int(E, – E2) = Int(E,) – Int(E2) %3D %3D %3D

Advanced Engineering Mathematics
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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Ex: Let (X, d) be a metric space and E, andE2 C X Show that whether each one of the following statement true or false or not and why. 1. Int(E, U E2) = Int(E,) U Int(E2) 2. Int(E, n E2) = Int(E,) n Int(E2) 3. Int(E, – E2) = Int(E,) – Int(E2) 4. Ə(E, U E2) = a(E,) U a(E2) 5. a(E, N E2) = a(E,) n a (E2) 6. Ə(E, – E2) = a(E,) – Ə(E2) 7. (E, U E2)' = (E,)'U (E2)' 8. (E_1nE_2 )' = (E,)' n (E2)" 9. (E – E2)' = (E,)' – (E2)' %3D | 10. (E, U E2) = (E,) U (E2) 11. (E, n E2) = E n (E2 12. (E, — Е2) (E,) (E2) %D - 13.E,=E, 14.Int(Int(E,)) = Int(E,)
Transcribed Image Text:Ex: Let (X, d) be a metric space and E, andE2 C X Show that whether each one of the following statement true or false or not and why. 1. Int(E, U E2) = Int(E,) U Int(E2) 2. Int(E, n E2) = Int(E,) n Int(E2) 3. Int(E, – E2) = Int(E,) – Int(E2) 4. Ə(E, U E2) = a(E,) U a(E2) 5. a(E, N E2) = a(E,) n a (E2) 6. Ə(E, – E2) = a(E,) – Ə(E2) 7. (E, U E2)' = (E,)'U (E2)' 8. (E_1nE_2 )' = (E,)' n (E2)" 9. (E – E2)' = (E,)' – (E2)' %3D | 10. (E, U E2) = (E,) U (E2) 11. (E, n E2) = E n (E2 12. (E, — Е2) (E,) (E2) %D - 13.E,=E, 14.Int(Int(E,)) = Int(E,)
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