H 6. Prove that the distinct equivalence classes of the relation of congruence modulo n are the sets [0], [1], [2], ..., where for each a = 0, 1, 2, ..., n - 1, [a] = {m e Z | m = a (mod n)}. 1
H 6. Prove that the distinct equivalence classes of the relation of congruence modulo n are the sets [0], [1], [2], ..., where for each a = 0, 1, 2, ..., n - 1, [a] = {m e Z | m = a (mod n)}. 1
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 4E: 4. Let be the relation “congruence modulo 5” defined on as follows: is congruent to modulo if...
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![H 6. Prove that the distinct equivalence classes of the relation of
congruence modulo n are the sets [0], [1], [2], ...,
where for each a = 0, 1, 2,..., n - 1,
[a] = {m e Z | m = a (mod n)}.
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e6203f-f751-4558-ba33-f371cf952d2b%2F97a21b6f-e3c4-4656-ae56-bdc9ce65cd2f%2Fs83sazf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:H 6. Prove that the distinct equivalence classes of the relation of
congruence modulo n are the sets [0], [1], [2], ...,
where for each a = 0, 1, 2,..., n - 1,
[a] = {m e Z | m = a (mod n)}.
1
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