For every nonempty set A, there exists a relation R which is both an equivalence relation and a partial ordering on A.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...
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For every nonempty set A, there exists a relation R which is both an equivalence relation
and a partial ordering on A.

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