Respuesta :
The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .
In the question ,
it is given that ,
Option(a) ,
R is a relation on set of all people where (a,b) is in R if a is taller than b .
Reflexive : NO , because "a" cannot be taller than "a" itself .
Symmetric : NO , because if "a" is taller than "b" , then "b" will be shorter than "a" .
Transitive : YES , because if "a" is taller than "b" and "b" is taller than "c" , then "a" is taller than "c" .
Option(b)
R is a relation on set of integers > 0 where (a,b) is in R if a divides b .
Reflexive : YES , because every number divides itself .
Symmetric : NO , because if "a" divided "b" , then "b" may not divide "a" .
Transitive : YES , because if "a" divided "b" and "b" divides "c" , then "a" must divide "c" .
Option(c)
R is a relation on set of all people where (a,b) is in R if a is married to b .
Reflexive : NO , because marriage is between two people , and "a" cannot marry "a" .
Symmetric : YES , because if "a" is married to "b" , then "b" is married to "a" .
Transitive : NO , because if "a" is married to "b" and "b" is married to "c" , then "a" is not married to "c" .
Therefore , The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .
The given question is incomplete , the complete question is
Write in the space provided the property or properties that each relation possesses (reflexive, symmetric, transitive).
(a) R is a relation on the set of all people, (a,b) is in R if a is taller than b .
(b) R is a relation on the set of integers > 0 , (a,b) is in R if a divides b .
(c) R is a relation on the set of all people , (a,b) is in R if a is married to b .
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