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Let X = {a, b, c}. For each of the following binary relations on X, check the boxes next to the properties that the relation has. Select all that apply! (a) 0 = { } O reflexive O symmetric O antisymmetric O transitive (b) 9%3D {(а, а), (b, b), (с, с)} O symmetric O reflexive antisymmetric transitive {(а, а), (b, а), (b, b), (с, а), (с, b), (с, с)} O symmetric (c) A O reflexive O antisymmetric O transitive (d) X х Х%— {(а, а), (а, b), (а, с), (b, a), (b, b), (Ь, с), (с, а), (с, b), (с, с)} O reflexive O symmetric O antisymmetric O transitive (е) (X х X) \ %3 {(а, b), (а, с), (b, а), (b, с), (с, а), (с, b)} O reflexive O symmetric O antisymmetric O transitive

Let X = {a, b, c}. For each of the following binary relations on X, check the boxes next to the properties that the relation has. Select all that apply! (a) 0 = { } O reflexive O symmetric O antisymmetric O transitive (b) 9%3D {(а, а), (b, b), (с, с)} O symmetric O reflexive antisymmetric transitive {(а, а), (b, а), (b, b), (с, а), (с, b), (с, с)} O symmetric (c) A O reflexive O antisymmetric O transitive (d) X х Х%— {(а, а), (а, b), (а, с), (b, a), (b, b), (Ь, с), (с, а), (с, b), (с, с)} O reflexive O symmetric O antisymmetric O transitive (е) (X х X) \ %3 {(а, b), (а, с), (b, а), (b, с), (с, а), (с, b)} O reflexive O symmetric O antisymmetric O transitive

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...
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Let X = {a, b, c}. For each of the following binary relations on X, check the boxes next to the properties that the relation has. Select all that apply! (a) 0 = { } O reflexive O symmetric O antisymmetric O transitive (b) D {(а, а), (b, b), (с, с)} O reflexive O symmetric antisymmetric transitive {(а, а), (b, а), (b, b), (с, а), (с, b), (с, с)} O symmetric (c) A O reflexive O antisymmetric O transitive (d) X х Х— {(а, а), (а, ), (а, с), (b, a), (b, b), (Ь, с), (с, а), (с, b), (с, с)} O reflexive O symmetric O antisymmetric O transitive (е) (X x X) \9%- {(а, b), (а, с), (b, а), (b, с), (с, а), (с, b)} O reflexive O symmetric O antisymmetric O transitive
Transcribed Image Text:Let X = {a, b, c}. For each of the following binary relations on X, check the boxes next to the properties that the relation has. Select all that apply! (a) 0 = { } O reflexive O symmetric O antisymmetric O transitive (b) D {(а, а), (b, b), (с, с)} O reflexive O symmetric antisymmetric transitive {(а, а), (b, а), (b, b), (с, а), (с, b), (с, с)} O symmetric (c) A O reflexive O antisymmetric O transitive (d) X х Х— {(а, а), (а, ), (а, с), (b, a), (b, b), (Ь, с), (с, а), (с, b), (с, с)} O reflexive O symmetric O antisymmetric O transitive (е) (X x X) \9%- {(а, b), (а, с), (b, а), (b, с), (с, а), (с, b)} O reflexive O symmetric O antisymmetric O transitive
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