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To find: the equivalence relation.
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Answer to Problem 15WE
A relation such as “Is as rusty as” that is reflexive, symmetric and transitive is an equivalence relation then “has the same length as” is equivalence relation. Option “b” is correct.
Explanation of Solution
Given information:
Given relations are
- Has rustier than
- Has the same length as
- Is opposite (for rays)
- Is coplanar with (for lines)
Calculation:
Reflexive property: Robot A is as rusty as itself.
Symmetric property: If Robot A is as rusty as Robot B then Robot B is as rusty as Robot A.
Transitive property: If Robot A is as rusty as Robot B and Robot B is as rusty as Robot C, then Robot A is as rusty as Robot C.
A relation such as “Is as rusty as” that is reflexive, symmetric and transitive is an equivalence relation then “has the same length as” is equivalence relation. Option “b” is correct.
Chapter 2 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning
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