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Let A equal the set of all strings of O's, 1's, and 2's that have length 4 and for which the sum of the characters in the string is less than or equal to 2. Define a relation R on . as follows: For every s, t e A, s Rt e the sum of the characters of s equals the sum of the characters of t. It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

Let A equal the set of all strings of O's, 1's, and 2's that have length 4 and for which the sum of the characters in the string is less than or equal to 2. Define a relation R on . as follows: For every s, t e A, s Rt e the sum of the characters of s equals the sum of the characters of t. It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)

Advanced Engineering Mathematics
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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Can you give me the correct answer to "It is a fact that R is an equivalence relation on A. Use set-roster notation to list the distinct equivalence classes of R. (Enter your answer as a comma-separated list of sets.)"? Original Problem Statement as an image.

**Title: Understanding Equivalence Relations on Strings** **Description:** Let \( A \) equal the set of all strings of 0's, 1's, and 2's that have length 4 and for which the sum of the characters in the string is less than or equal to 2. Define a relation \( R \) on \( A \) as follows: For every \( s, \, t \in A \), \( s \, R \, t \iff \) the sum of the characters of \( s \) equals the sum of the characters of \( t \). It is a fact that \( R \) is an equivalence relation on \( A \). Use set-roster notation to list the distinct equivalence classes of \( R \). (Enter your answer as a comma-separated list of sets.) **Detailed Explanation:** The problem states that there is a set \( A \) containing all strings of four characters consisting of 0's, 1's, and 2's, with the constraint that the sum of the character values in each string does not exceed 2. An equivalence relation \( R \) is defined such that two strings \( s \) and \( t \) are related if they have the same sum of character values. The task is to determine the distinct equivalence classes formed by this relation, using set-roster notation. Each equivalence class will group strings that yield the same character sum.
Transcribed Image Text:**Title: Understanding Equivalence Relations on Strings** **Description:** Let \( A \) equal the set of all strings of 0's, 1's, and 2's that have length 4 and for which the sum of the characters in the string is less than or equal to 2. Define a relation \( R \) on \( A \) as follows: For every \( s, \, t \in A \), \( s \, R \, t \iff \) the sum of the characters of \( s \) equals the sum of the characters of \( t \). It is a fact that \( R \) is an equivalence relation on \( A \). Use set-roster notation to list the distinct equivalence classes of \( R \). (Enter your answer as a comma-separated list of sets.) **Detailed Explanation:** The problem states that there is a set \( A \) containing all strings of four characters consisting of 0's, 1's, and 2's, with the constraint that the sum of the character values in each string does not exceed 2. An equivalence relation \( R \) is defined such that two strings \( s \) and \( t \) are related if they have the same sum of character values. The task is to determine the distinct equivalence classes formed by this relation, using set-roster notation. Each equivalence class will group strings that yield the same character sum.
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