2. For each equivalence relation below, find the requested equivalence class. a. R = { (1,1), (1, 3), (3, 1), (2, 2), (3, 3), (4, 4)} on {1,2,3,4}. Find [1]. b. R = { (1,1), (1,3), (3, 1), (2, 2), (3,3), (4, 4)} on {1,2, 3, 4}. Find [4]. c. Ris has-the-same-tens-digit-as on the set {xeZ : 100 < x < 200}. Find [132].
2. For each equivalence relation below, find the requested equivalence class. a. R = { (1,1), (1, 3), (3, 1), (2, 2), (3, 3), (4, 4)} on {1,2,3,4}. Find [1]. b. R = { (1,1), (1,3), (3, 1), (2, 2), (3,3), (4, 4)} on {1,2, 3, 4}. Find [4]. c. Ris has-the-same-tens-digit-as on the set {xeZ : 100 < x < 200}. Find [132].
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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Please help with math in image. Thank you.
![### Equivalence Relations Problem Set
#### Problem 2
For each equivalence relation below, find the requested equivalence class.
**a.** Let \( R = \{ (1, 1), (1, 3), (3, 1), (2, 2), (3, 3), (4, 4) \} \) on the set \(\{1, 2, 3, 4\}\). Find the equivalence class \([1]\).
**b.** Let \( R = \{ (1, 1), (1, 3), (3, 1), (2, 2), (3, 3), (4, 4) \} \) on the set \(\{1, 2, 3, 4\}\). Find the equivalence class \([4]\).
**c.** \( R \) is defined as "has-the-same-tens-digit-as" on the set \(\{x \in \mathbb{Z} : 100 < x < 200\}\). Find the equivalence class \([132]\).
**d.** \( R \) is defined as "has-the-same-parents-as" on the set of all human beings. Find the equivalence class \([you]\).
---
The problems above involve finding equivalence classes for given equivalence relations. An equivalence class is a subset of a set formed by elements that are equivalent to each other under a given relation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F620c60a1-10fe-416e-8b85-1e75a34b227e%2F50921302-0414-43ec-837d-2a86f8295544%2F65nprgl_processed.png&w=3840&q=75)
Transcribed Image Text:### Equivalence Relations Problem Set
#### Problem 2
For each equivalence relation below, find the requested equivalence class.
**a.** Let \( R = \{ (1, 1), (1, 3), (3, 1), (2, 2), (3, 3), (4, 4) \} \) on the set \(\{1, 2, 3, 4\}\). Find the equivalence class \([1]\).
**b.** Let \( R = \{ (1, 1), (1, 3), (3, 1), (2, 2), (3, 3), (4, 4) \} \) on the set \(\{1, 2, 3, 4\}\). Find the equivalence class \([4]\).
**c.** \( R \) is defined as "has-the-same-tens-digit-as" on the set \(\{x \in \mathbb{Z} : 100 < x < 200\}\). Find the equivalence class \([132]\).
**d.** \( R \) is defined as "has-the-same-parents-as" on the set of all human beings. Find the equivalence class \([you]\).
---
The problems above involve finding equivalence classes for given equivalence relations. An equivalence class is a subset of a set formed by elements that are equivalent to each other under a given relation.
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