Let A = {1, 2, 3, 4). Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4,3)} An arrow diagram and matrix representation of the relation are supposed to be represented below, but there are some mistakes. Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right. 1 4 2 3 1) Which pair is in the arrow diagram but not the original R? Give your answer in the form (a b) 0 1 0 0 1 0 0 0 0 0 1 1 Incorrect Look at arrows leaving 3. 0 1 1 0 Yo ४ O W 17
Let A = {1, 2, 3, 4). Define a relation R on A: R = {(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4,3)} An arrow diagram and matrix representation of the relation are supposed to be represented below, but there are some mistakes. Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right. 1 4 2 3 1) Which pair is in the arrow diagram but not the original R? Give your answer in the form (a b) 0 1 0 0 1 0 0 0 0 0 1 1 Incorrect Look at arrows leaving 3. 0 1 1 0 Yo ४ O W 17
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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![**Matrix Relations and Corrections Exercise**
**Question 2:**
Which pair is in the original set R but not represented in the arrow diagram? Give your answer in the form (a, b).
[Input Box]
*Button:* Check | *Link:* Show answer
---
**Question 3:**
Which entry in the matrix is a 0 but should be a 1? Give your answer in the form (row-number, column-number). Note that the correct relation is given by the set R.
[Input Box]
*Button:* Check | *Link:* Show answer
---
**Question 4:**
Which entry in the matrix is a 1 but should be a 0? Give your answer in the form (row-number, column-number). Note that the correct relation is given by the set R.
[Input Box]
*Button:* Check | *Link:* Show answer
---
**Instructions:**
- Review the matrix and arrow diagram to determine the correct entries.
- Use the provided input boxes to submit your answers.
- Click "Check" to verify your answers, or "Show answer" to reveal the correct response if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bb27111-b1b5-4971-bf31-10d5c3bec1a4%2Fab6bd57b-a41b-4923-863c-0562d6266bc1%2Fg4oee6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Relations and Corrections Exercise**
**Question 2:**
Which pair is in the original set R but not represented in the arrow diagram? Give your answer in the form (a, b).
[Input Box]
*Button:* Check | *Link:* Show answer
---
**Question 3:**
Which entry in the matrix is a 0 but should be a 1? Give your answer in the form (row-number, column-number). Note that the correct relation is given by the set R.
[Input Box]
*Button:* Check | *Link:* Show answer
---
**Question 4:**
Which entry in the matrix is a 1 but should be a 0? Give your answer in the form (row-number, column-number). Note that the correct relation is given by the set R.
[Input Box]
*Button:* Check | *Link:* Show answer
---
**Instructions:**
- Review the matrix and arrow diagram to determine the correct entries.
- Use the provided input boxes to submit your answers.
- Click "Check" to verify your answers, or "Show answer" to reveal the correct response if needed.
![**Participation Activity: Representations of Binary Relations on a Set**
**Let \( A = \{1, 2, 3, 4\} \). Define a relation \( R \) on \( A \):**
\[ R = \{(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4, 3)\} \]
An arrow diagram and matrix representation of the relation are supposed to be represented below, *but there are some mistakes.*
Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right.
**Arrow Diagram:**
- The arrow diagram visually represents the relations.
- The nodes are labeled 1 through 4.
- Arrows indicate the presence of a relation from one element to another.
**Matrix Representation:**
- A \(4 \times 4\) matrix representation is shown.
\[
\begin{bmatrix}
0 & 1 & 1 & 0 \\
0 & 1 & 1 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
\end{bmatrix}
\]
**Analysis Task:**
1) Which pair is in the arrow diagram but not in the original \( R \)? Provide your answer in the form \((a, b)\).
**Hint for Correction:**
- Check the arrows originating from node 3 for potential discrepancies.
**Input Field:**
- [ ] Check
**Feedback:**
- "Incorrect" - Look at arrows leaving 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bb27111-b1b5-4971-bf31-10d5c3bec1a4%2Fab6bd57b-a41b-4923-863c-0562d6266bc1%2Fzovk4r4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Participation Activity: Representations of Binary Relations on a Set**
**Let \( A = \{1, 2, 3, 4\} \). Define a relation \( R \) on \( A \):**
\[ R = \{(1, 2), (1, 3), (2, 2), (2, 3), (3, 4), (4, 3)\} \]
An arrow diagram and matrix representation of the relation are supposed to be represented below, *but there are some mistakes.*
Rows of the matrix are numbered 1 through 4 from top to bottom and columns are numbered 1 through 4 from left to right.
**Arrow Diagram:**
- The arrow diagram visually represents the relations.
- The nodes are labeled 1 through 4.
- Arrows indicate the presence of a relation from one element to another.
**Matrix Representation:**
- A \(4 \times 4\) matrix representation is shown.
\[
\begin{bmatrix}
0 & 1 & 1 & 0 \\
0 & 1 & 1 & 0 \\
0 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 \\
\end{bmatrix}
\]
**Analysis Task:**
1) Which pair is in the arrow diagram but not in the original \( R \)? Provide your answer in the form \((a, b)\).
**Hint for Correction:**
- Check the arrows originating from node 3 for potential discrepancies.
**Input Field:**
- [ ] Check
**Feedback:**
- "Incorrect" - Look at arrows leaving 3.
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