The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1, 00). Can X1, X2, X3 be equivalence classes with respect to some equivalence relation on R? O No, they can't be equivalence classes for some equivalence relation since X1n X2 + 0. O No, they can't be equivalence classes for some equivalence relation since any equivalence relation on infinite set has infinitely many different equivalence classes. O Yes, these sets can be equivalence classes for some equivalence relation since X1 U X2 U X3 = R. O Yes, these sets can be equivalence classes for some equivalence relation since X2n X3 = 0.
The real line R is divided into subsets X1, X2, X3 where X1 = (-00, – 7], X2 = [-7,1), and X3 = [1, 00). Can X1, X2, X3 be equivalence classes with respect to some equivalence relation on R? O No, they can't be equivalence classes for some equivalence relation since X1n X2 + 0. O No, they can't be equivalence classes for some equivalence relation since any equivalence relation on infinite set has infinitely many different equivalence classes. O Yes, these sets can be equivalence classes for some equivalence relation since X1 U X2 U X3 = R. O Yes, these sets can be equivalence classes for some equivalence relation since X2n X3 = 0.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 28E
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