Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} and define a relation R on A as follows: For all x, y E A, x R y ↔ 3|(x - y). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [0] [1] = [2] = [3] = = How many distinct equivalence classes does R have? classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} and define a relation R on A as follows: For all x, y E A, x R y ↔ 3|(x - y). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [0] [1] = [2] = [3] = = How many distinct equivalence classes does R have? classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} and define a relation R on A as follows:
For all x, y EA, x Ry⇒ 3|(x - y).
It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R.
[0]
[1]
II
[3]
=
[2] =
=
How many distinct equivalence classes does R have?
classes
List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a2c9ae4-718a-4288-bbc7-9ce9838a8ae1%2Fd7cba7e6-a5f6-48c8-a91a-a0f199ee42f8%2Fv5mxmm_processed.png&w=3840&q=75)
Transcribed Image Text:Let A = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4} and define a relation R on A as follows:
For all x, y EA, x Ry⇒ 3|(x - y).
It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R.
[0]
[1]
II
[3]
=
[2] =
=
How many distinct equivalence classes does R have?
classes
List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
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