My text book is currently asking this question:

"Are these system specifications consistent? Whenever the system software is being upgraded, users cannot access the file system. If users can access the file system, then they can save new files. If users cannot save new files, then the system software is not being upgraded.

I am not allowed to use a truth table. Currently, this is what I have.

u = system is upgraded

a = access system file

s = save new files

(u a) (a s) ( s u)

1. u a Hypothesis
2. a s Hypothesis
3. a s Inverse step 1
4. u s Hypothetical syllogism step 1 and 3
5. ???

I am uncertain as to how to proceed. I know the answer is that the system is consistent, but I am not sure how to prove this without a truth table or something similar.