Question

Are these system specifications 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.”

Short answer

From the given statements, the systems are consistent.

Step-by-step solution

Introduction to the Concept

When two propositions can both be true at the same time, they are said to be consistent. Perform a joint truth test to ensure consistency.

Given statements

The given statements are given as,

Statement 1: If the file system is not locked, then new messages will be queued

~p→q

Statement 2: If the file system is not locked, then the system is functioning normally, and conversely.

p↔r

Statement 3: If new messages are not queued, then they will be sent to the message buffer.

~q→s

Statement 4: If the file system is not locked, then new messages will be sent to the message buffer.

~p→s

Statement 5: New messages will not be sent to the message buffer.

~s

Solution Explanation

From the given statements, the system specifications are translated as given below,

1) p→q

2) r→q

3) r→p

4) ~q

Take to be false in order to make ~r to be true to achieve consistency.

Because of the two conditional statements that follow, this necessarily states that both p and q are true.

The first conditional statement, ~p→q, is true and has the form $\mathrm{F}\to \mathrm{T}$.

Finally, we can satisfy ~p→q by assuming that s is false.

As a result, these requirements are consistent.