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7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a › {A0, A1,..., An,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! Prove that U A; is countable. Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words. (b) (c)

7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a › {A0, A1,..., An,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! Prove that U A; is countable. Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words. (b) (c)

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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7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a {A0, A₁,..., An,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! 8. (b) (c) Prove that U20 A, is countable. Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words. Prove that the relation between sets is symmetric and transitive.
Transcribed Image Text:7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a {A0, A₁,..., An,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! 8. (b) (c) Prove that U20 A, is countable. Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words. Prove that the relation between sets is symmetric and transitive.
7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a {A0, A₁,..., An,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! 8. (b) (c) Prove that U20 A, is countable. Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words. Prove that the relation between sets is symmetric and transitive.
Transcribed Image Text:7. Suppose we know that each of An, n ≥ 0, is countable. Show that (a {A0, A₁,..., An,...} is a set. If you used some of the Principles 0-3 in this subquestion, be explicit! 8. (b) (c) Prove that U20 A, is countable. Did you need the Axiom of Choice in any of the sub- questions here? Explain clearly in a FEW words. Prove that the relation between sets is symmetric and transitive.
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