Let X = [0, 1]. Consider the following claim: “For every complete binary relation on a non-empty set X, there exists a subset A of X that has a greatest element.” Is this statement true or false? If true provide a proof, if false provide a counterexample.
Let X = [0, 1]. Consider the following claim: “For every complete binary relation on a non-empty set X, there exists a subset A of X that has a greatest element.” Is this statement true or false? If true provide a proof, if false provide a counterexample.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 15E: 15. Let be a binary operation on the non empty set . Prove that if contains an identity element...
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Let X = [0, 1]. Consider the following claim: “For every complete binary relation on a non-empty set X, there exists a subset A of X that has a greatest element.” Is this statement true or false? If true provide a proof, if false provide a counterexample.
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