Define a relation R on Z as follows: For all integers m and n, 51(m² - n²). mRn (a) Is 1 R (-4)? Yes No (b) Is 2 R 12? Yes No (c) Is 2 R (-7)? Yes No (d) Is (-7) R 2? Yes O No
Define a relation R on Z as follows: For all integers m and n, 51(m² - n²). mRn (a) Is 1 R (-4)? Yes No (b) Is 2 R 12? Yes No (c) Is 2 R (-7)? Yes No (d) Is (-7) R 2? Yes O No
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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![Define a relation \( R \) on \(\mathbb{Z}\) as follows: For all integers \( m \) and \( n \),
\[ m \, R \, n \iff 5|(m^2 - n^2). \]
### Questions
(a) Is \( 1 \, R \, (-4) \)?
- ○ Yes
- ○ No
(b) Is \( 2 \, R \, 12 \)?
- ○ Yes
- ○ No
(c) Is \( 2 \, R \, (-7) \)?
- ○ Yes
- ○ No
(d) Is \((-7) \, R \, 2 \)?
- ○ Yes
- ○ No](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc8ef3851-b223-4be3-ac39-739e48c0c7a3%2F8cc1eb62-f242-4381-9bbd-a6c70539fc27%2Fv5t63oo_processed.png&w=3840&q=75)
Transcribed Image Text:Define a relation \( R \) on \(\mathbb{Z}\) as follows: For all integers \( m \) and \( n \),
\[ m \, R \, n \iff 5|(m^2 - n^2). \]
### Questions
(a) Is \( 1 \, R \, (-4) \)?
- ○ Yes
- ○ No
(b) Is \( 2 \, R \, 12 \)?
- ○ Yes
- ○ No
(c) Is \( 2 \, R \, (-7) \)?
- ○ Yes
- ○ No
(d) Is \((-7) \, R \, 2 \)?
- ○ Yes
- ○ No
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