A technician suspects that one or more of the processors in a distributed system is not working properly. The processors, A, B, and C, are all capable of reporting information about the status (working or not working) of the processors in the system. The technician is unsure whether a processor is really not working, or whether the problem is in the status reporting routines in one or more of the processors. After polling each processor, the technician receives the following status reports: • Processor A reports that processor B is not working and processor C is working. • Processor B reports that A is working if and only if B is working. Processor C reports that at least one of the other processors is not working.
A technician suspects that one or more of the processors in a distributed system is not working properly. The processors, A, B, and C, are all capable of reporting information about the status (working or not working) of the processors in the system. The technician is unsure whether a processor is really not working, or whether the problem is in the status reporting routines in one or more of the processors. After polling each processor, the technician receives the following status reports: • Processor A reports that processor B is not working and processor C is working. • Processor B reports that A is working if and only if B is working. Processor C reports that at least one of the other processors is not working.
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 dont reject the question. I just need problem number "k".
![**Problem Statement:**
A technician suspects that one or more of the processors in a distributed system is not working properly. The processors, A, B, and C, are all capable of reporting information about the status (working or not working) of the processors in the system. The technician is unsure whether a processor is really not working, or whether the problem is in the status reporting routines in one or more of the processors. After polling each processor, the technician receives the following status reports:
- Processor A reports that processor B is not working and processor C is working.
- Processor B reports that A is working if and only if B is working.
- Processor C reports that at least one of the other processors is not working.
**Tasks:**
f. Let \( a = \) "A is working", \( b = \) "B is working", and \( c = \) "C is working." Write the three status reports in terms of \( a, b, \) and \( c \) and using the logical connectives.
- **A's report:**
- **B's report:**
- **C's report:**
g. Complete the following truth table:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
a & b & c & \text{A's report} & \text{B's report} & \text{C's report} \\
\hline
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
\hline
\end{array}
\]
h. Assuming that all of the status reports are true, which processor(s) is/are working? Justify your reasoning.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0057af3f-cb2f-462a-9497-d1179ce88e8c%2F1ae0291f-5e78-498c-bc88-8f374a521834%2Fab3aii_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A technician suspects that one or more of the processors in a distributed system is not working properly. The processors, A, B, and C, are all capable of reporting information about the status (working or not working) of the processors in the system. The technician is unsure whether a processor is really not working, or whether the problem is in the status reporting routines in one or more of the processors. After polling each processor, the technician receives the following status reports:
- Processor A reports that processor B is not working and processor C is working.
- Processor B reports that A is working if and only if B is working.
- Processor C reports that at least one of the other processors is not working.
**Tasks:**
f. Let \( a = \) "A is working", \( b = \) "B is working", and \( c = \) "C is working." Write the three status reports in terms of \( a, b, \) and \( c \) and using the logical connectives.
- **A's report:**
- **B's report:**
- **C's report:**
g. Complete the following truth table:
\[
\begin{array}{|c|c|c|c|c|c|}
\hline
a & b & c & \text{A's report} & \text{B's report} & \text{C's report} \\
\hline
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
& & & & & \\
\hline
\end{array}
\]
h. Assuming that all of the status reports are true, which processor(s) is/are working? Justify your reasoning.
Transcribed Image Text:### Educational Resource: Logic and Truth Tables
#### Task g:
**Complete the following truth table:**
| a | b | c | A’s report | B’s report | C’s report |
|---|---|---|------------|------------|------------|
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
#### Task h:
**Assuming that all of the status reports are true, which processor(s) is/are working? Justify your reasoning.**
#### Task i:
**Assuming that all of the processors are working, which status report(s) is/are false? Justify your reasoning.**
#### Task j:
**Assuming that a processor’s status report is true if and only if the processor is working, what is the status of each processor? Hint: construct a new truth table for this biconditional statement.**
#### Task k:
**Consider A’s report, B’s report, and C’s report as premises to an argument. Which of the following conclusions are valid: ¬a, ¬b, or ¬c? Use a truth table and explain your reasoning.**
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