# DISCRETE MATH: Are these system specifications consistent?

1. Homework Statement

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

2. Homework Equations

p = "The system software is being upgraded"

q = "Users can access the file system"

r = "Users can save new files"

3. The Attempt at a Solution

a) $$p\,\longrightarrow\,\neg\,q$$

b) $$q\,\longrightarrow\,r$$

c) $$\neg\,r\,\longrightarrow\,\neg\,p$$

Using truth tables for the above clauses, I found an assignment that makes the clauses all true. Make p = FALSE, q = TRUE, and r = TRUE. I say the system specification is consistent.

What do you think?

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AKG
Homework Helper
Yes, that works.

The clauses a) b) and C) are correct as well?

AKG