4. Let X be an ordered set, and A C X . Show that (a) For every x, x has at most one immediate 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
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 22E
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4. Let X be an ordered set, and A C X . Show that
(a) For every x, x has at most one immediate 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:4. Let X be an ordered set, and A C X . Show that (a) For every x, x has at most one immediate 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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