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. 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: b. Complete the following truth table: a b c A's report B's report C's report e. Assuming that a processor’s status report is true if and only if the processor is working, what is the status of each processor? Construct a new truth table for this biconditional statement. c. Assuming that all of the status reports are true, which processor(s) is/are working? d. Assuming that all of the processors are working, which status report(s) is/are false?
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. 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:
b. Complete the following truth table:
| a | b | c | A's report | B's report | C's report |
e. Assuming that a processor’s status report is true if and only if the processor is working, what is the status of each processor? Construct a new truth table for this biconditional statement.
c. Assuming that all of the status reports are true, which processor(s) is/are working?
d. Assuming that all of the processors are working, which status report(s) is/are false?
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 5 images
