Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(a, b) ∣ a and b are the same age} b) {(a, b) ∣ a and b have the same parents} c) {(a, b) ∣ a and b share a common parent}
Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack. a) {(a, b) ∣ a and b are the same age} b) {(a, b) ∣ a and b have the same parents} c) {(a, b) ∣ a and b share a common parent}
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 8E: In Exercises 610, a relation R is defined on the set Z of all integers. In each case, prove that R...
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Which of these relations on the set of all people are equivalence relations? Determine the properties of an equivalence relation that the others lack.
a) {(a, b) ∣ a and b are the same age}
b) {(a, b) ∣ a and b have the same parents}
c) {(a, b) ∣ a and b share a common parent}
d) {(a, b) ∣ a and b have met}
e) {(a, b) ∣ a and b speak a common language}
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