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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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