The "= mod n" relation on Z is transitive. Show that it is also symmetric and reflexive. Symmetry: Suppose a = b mod n. Then a = b + kn for some k, so b = a Reflexivity: For any a, a = a +0. n, so a = a mod 0 - kn, which means that b = a mod a
The "= mod n" relation on Z is transitive. Show that it is also symmetric and reflexive. Symmetry: Suppose a = b mod n. Then a = b + kn for some k, so b = a Reflexivity: For any a, a = a +0. n, so a = a mod 0 - kn, which means that b = a mod a
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Need help one with symmetry and reflex
![The "= mod n" relation on Z is transitive. Show that it is also symmetric and reflexive.
Symmetry: Suppose a = b mod n. Then a = b + kn for some k, so b = a
Reflexivity: For any a, a = a +0. n, so a = a mod 0
- kn, which means that b = a mod a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49655a96-3dec-4fd2-a317-d4fff3ba2079%2Fe9b097e6-435f-46fa-a729-b57a04d9c4e0%2Fpweb4b8_processed.png&w=3840&q=75)
Transcribed Image Text:The "= mod n" relation on Z is transitive. Show that it is also symmetric and reflexive.
Symmetry: Suppose a = b mod n. Then a = b + kn for some k, so b = a
Reflexivity: For any a, a = a +0. n, so a = a mod 0
- kn, which means that b = a mod a
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