Let A = {1, 2, 3, 4, ..., 22} and define a relation R on A as follows: For all x, y E A, x R y → 4|(x – ). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [1] = [2] = [3] = [4] [5] = 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 = {1, 2, 3, 4, ..., 22} and define a relation R on A as follows: For all x, y E A, x R y → 4|(x – ). It is a fact that R is an equivalence relation on A. Use set-roster notation to write the equivalence classes of R. [1] = [2] = [3] = [4] [5] = 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 = {1, 2, 3, 4, , 22} and define a relation R on A as follows:
For all x, y ∈ A, x R y ⇔ 4|(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.
How many distinct equivalence classes does R have?
List the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)
![Let \( A = \{ 1, 2, 3, 4, \ldots, 22 \} \) and define a relation \( R \) on \( A \) as follows:
For all \( x, y \in A \), \( x \, R \, y \iff 4|(x-y) \).
It is a fact that \( R \) is an equivalence relation on \( A \). Use set-roster notation to write the equivalence classes of \( R \).
\[ [1] = \boxed{} \]
\[ [2] = \boxed{} \]
\[ [3] = \boxed{} \]
\[ [4] = \boxed{} \]
\[ [5] = \boxed{} \]
How many distinct equivalence classes does \( R \) have?
\(\boxed{} \) classes
List the distinct equivalence classes of \( R \). (Enter your answer as a comma-separated list of sets.)
\(\boxed{} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fddb57a32-2247-47a5-9d55-8c5fe5ac9cfb%2F57eb21fa-ec78-473e-b974-527177ffbca3%2Fpzdsr3m_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( A = \{ 1, 2, 3, 4, \ldots, 22 \} \) and define a relation \( R \) on \( A \) as follows:
For all \( x, y \in A \), \( x \, R \, y \iff 4|(x-y) \).
It is a fact that \( R \) is an equivalence relation on \( A \). Use set-roster notation to write the equivalence classes of \( R \).
\[ [1] = \boxed{} \]
\[ [2] = \boxed{} \]
\[ [3] = \boxed{} \]
\[ [4] = \boxed{} \]
\[ [5] = \boxed{} \]
How many distinct equivalence classes does \( R \) have?
\(\boxed{} \) classes
List the distinct equivalence classes of \( R \). (Enter your answer as a comma-separated list of sets.)
\(\boxed{} \)
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