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13. Let (X,<) be a partially ordered set, and let X 0. Indicate the condition that guarantees the existence of a maximal element in (X, <): a. (X,) is a linearly ordered set. b. X is a finite set, or every linearly ordered subset of X has an upper bound. c. (X,) is a well-ordered set. d. There exists a minimal element in (X, ≤).

13. Let (X,<) be a partially ordered set, and let X 0. Indicate the condition that guarantees the existence of a maximal element in (X, <): a. (X,) is a linearly ordered set. b. X is a finite set, or every linearly ordered subset of X has an upper bound. c. (X,) is a well-ordered set. d. There exists a minimal element in (X, ≤).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 20E: Give an example of a relation R on a nonempty set A that is symmetric and transitive, but not...
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13. Let (X,<) be a partially ordered set, and let X 0. Indicate the condition that guarantees the existence of a maximal element in (X, <): a. (X,) is a linearly ordered set. b. X is a finite set, or every linearly ordered subset of X has an upper bound. c. (X,) is a well-ordered set. d. There exists a minimal element in (X, ≤).
Transcribed Image Text:13. Let (X,<) be a partially ordered set, and let X 0. Indicate the condition that guarantees the existence of a maximal element in (X, <): a. (X,) is a linearly ordered set. b. X is a finite set, or every linearly ordered subset of X has an upper bound. c. (X,) is a well-ordered set. d. There exists a minimal element in (X, ≤).
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