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Let X be an ordered set, and A C X. Show that a. for every E X, x has at most one immidiate successor and at most one immediate predecessor. b. Show that A has at most one smallest element and at most one largest element.

Let X be an ordered set, and A C X. Show that a. for every E X, x has at most one immidiate successor and at most one immediate predecessor. b. Show that A has at most one smallest element and at most one largest element.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.1: Sets
Problem 10E
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Let X be an ordered set, and A C X. Show that a. for every E X, x has at most one immidiate successor and at most one immediate predecessor. b. Show that A has at most one smallest element and at most one largest element.
Transcribed Image Text:Let X be an ordered set, and A C X. Show that a. for every E X, x has at most one immidiate successor and at most one immediate predecessor. b. Show that A has at most one smallest element and at most one largest element.
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