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The goal of this exercise is to determine whether the following system specifications are consistent: If the file system is not locked, then new messages will be queued. If the file system is not locked, then the system is functioning normally, and conversely. If new messages are not queued, then they will be sent to the message buffer. If the file system is not locked, then new messages will be sent to the message buffer. New messages will not be sent to the message buffer.

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Answer:

The following specifications are consistent

Step-by-step explanation:

The file system is locked ⇒ L

New messages will be queued ⇒ Q

The system is functioning normally ⇒ N

The message will be sent to the message buffer ⇒ B

" Now, let us rewrite the specifications"

"If the file system is not locked, then new messages will be queued" ∴ ¬L ⇒ Q

"If the system is not locked, then the system is functioning normally and conversely" ∴ ¬L ⇔ N

"If new messages are not queued, then they will be sent to the message buffer" ∴ ¬Q ⇒ B

"If the file system is not locked, then new messages will be sent to the message buffer" ∴ ¬L ⇒ B

"New messages will not be sent to the message buffer" ∴ ¬B

To get consistency, take N to be false such that ¬N is true.

This mean that both L and Q be true, by the two conditional statements that have N as consequence.

First conditional statement ¬L ⇒ Q is of the form F?T, which is true.

Finally, the ¬L ⇒ B can be satisfied by taking B to be false.

This means that this set of specifications is consistent!

Truth value assignment

B: False

N: False

Q: True

L: True

Observing the Specification, Condition and Truth Value, it is evident that they are consistent.

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