Answer
The system is consistent
Work Step by Step
We will check the consistency of the system specifications using a truth table.
Let $p$ denote "The system software is being updated, $q$ denote "Users can access the file system" and $r$ denote "Users can save new files".
The system specification are as follows:
Whenever the system software is being upgraded, users cannot access the file system - $ p \to \neg q$
If users can access the file system, then they can save new files - $q \to r$
If users cannot save new files, then the system software is not being upgraded - $\neg r \to \neg p$
The truth table:
\begin{array}{c|c|c|c|c|c|c |c}
p & q & r &p \to \neg q & q \to r & \neg r \to \neg p \\
T & T & T & F& T & T\\
T & T & F & F& F& F\\
T & F & T & T& T& T\\
T & F & F & T& T&F \\
F & T & T & T& T& T\\
F & T & F & T& F& T\\
F & F & T & T& T& T\\
F & F & F & T& T& T
\end{array}
Since a row exists where all three system specifications are true, the system specifications are consistent.
