Let A = {-3, –2, –1, 0, 1, 2, 3, 4, 5, 6} and define a relation R on A as follows: For all x, y E A, x R y 3|(x – ). 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? 3 classes List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
Let A = {-3, –2, –1, 0, 1, 2, 3, 4, 5, 6} and define a relation R on A as follows: For all x, y E A, x R y 3|(x – ). 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? 3 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 = {−3, −2, −1, 0, 1, 2, 3, 4, 5, 6} and define a relation R on A as follows:
For all x, y 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.
List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
![Let \( A = \{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6\} \) and define a relation \( R \) on \( A \) as follows:
For all \( x, y \in A \), \( x \, R \, y \iff 3 \mid (x - y) \).
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?
3 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%2Fddb57a32-2247-47a5-9d55-8c5fe5ac9cfb%2F8d0f4b19-0686-4ecb-a6d5-63ec23306214%2Fc4hk7jj_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( A = \{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6\} \) and define a relation \( R \) on \( A \) as follows:
For all \( x, y \in A \), \( x \, R \, y \iff 3 \mid (x - y) \).
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?
3 classes
List the distinct equivalence classes of \( R \). (Enter your answer as a comma-separated list of sets.)
\(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
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