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Description: Let F be a nontrivial on X. Prove that the follow-ing statements are equivalent1. F is an ultrafilter.2. (∀A⊆X)A∈F ↔ X−A∈/F.3. (∀A,B⊆X)A∪B∈F → A∈F or B∈F.

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Let F be a nontrivial on X. Prove that the follow- ing statements are equivalent1. F is an ultrafilter.2. (∀A⊆X)A∈F ↔ X−A∈/F.3. (∀A,B⊆X)A∪B∈F → A∈F or B∈F.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.

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Let F be a nontrivial on X. Prove that the follow-

ing statements are equivalent
1. F is an ultrafilter.
2. (∀A⊆X)A∈F ↔ X−A∈/F.
3. (∀A,B⊆X)A∪B∈F → A∈F or B∈F.

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