1. Find all cquivalent classes determined by congruence modulo 5 on Z.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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1. Find all cquivalent classes determined by congruence modulo 5 on Z.
Transcribed Image Text:1. Find all cquivalent classes determined by congruence modulo 5 on Z.
Expert Solution
Step 1

The equivalent classes under modulo n is defined by,

a=x: xamod nIn the question n=5a=x: xamod 5

athis is represent the equivalent class of a,

0=x: x0mod 5

Means in this those element are present in 0,

Which give reminder 0, when Multiple of 5. 

0=5k+00=...-5,0,5,10,15,....  

1=x: x1mod 5 

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