7. Let (a, b), (c,d) E R2. Define a relation ~on R² by (a, b) (c,d) if 2a - b = 2c-d. (a) Show that is an equivalence relation. (b) Find the equivalence class of (0, 1).
7. Let (a, b), (c,d) E R2. Define a relation ~on R² by (a, b) (c,d) if 2a - b = 2c-d. (a) Show that is an equivalence relation. (b) Find the equivalence class of (0, 1).
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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![**Problem 7**
Let \((a, b), (c, d) \in \mathbb{R}^2\). Define a relation \(\sim\) on \(\mathbb{R}^2\) by
\[
(a, b) \sim (c, d) \text{ if } 2a - b = 2c - d.
\]
(a) Show that \(\sim\) is an equivalence relation.
(b) Find the equivalence class of \((0, 1)\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd597ffd2-5c4b-4c2e-8332-77ce1607dac1%2F2aabd0f3-1b3c-4afc-baae-faa51d44c2c0%2Ftt8c0d8_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 7**
Let \((a, b), (c, d) \in \mathbb{R}^2\). Define a relation \(\sim\) on \(\mathbb{R}^2\) by
\[
(a, b) \sim (c, d) \text{ if } 2a - b = 2c - d.
\]
(a) Show that \(\sim\) is an equivalence relation.
(b) Find the equivalence class of \((0, 1)\).
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