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Let < be a partially order on a set A. Show that there exists a linear order 3 on A such that if a

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 4E: 4. Let , where is nonempty. Prove that a has left inverse if and only if for every subset of .

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Let < be a partially order on a set A. Show that there exists a linear order
3 on A such that if a <b (a, b E A), a 3 b.

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