Let A be a set and R = {(x, x) : x ∈ A} be the is-equal-to relation on A. Prove that a relation S on A is an equivalence relation and a partial ordering if and only if S = R.
Let A be a set and R = {(x, x) : x ∈ A} be the is-equal-to relation on A. Prove that a relation S on A is an equivalence relation and a partial ordering if and only if S = R.
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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10. Let A be a set and R = {(x, x) : x ∈ A} be the is-equal-to relation on A. Prove that a relation S on A is an equivalence relation and a partial ordering if and only if S = R.
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