How to check whether a set of statements is consistent

Question

When do you call a system is consistent?

Here's the system (it's consistent btw)

When a software is upgraded, user can't use the software

If user can use the software, user can save their file

If user can save their file, user can't upgrade the software

Answer 1

Hint

A system [theory, set of sentences] is consistent

"if and only if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true."

How to check if a set of sentences is consistent ? Try to find an interpretation under which all formulas in it are true.

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The logical form of the argument is :

if Grade, then not-Use:

if Use, then Save:

Therefore, if Save, then not-Grade.

We can use this for checking both consistency [i.e. satisfiability] and validity.