# Homework Help: DISCRETE MATH: Are these system specifications consistent?

1. Jan 9, 2007

### VinnyCee

1. The problem statement, all variables and given/known data

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. Relevant 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?

2. Jan 9, 2007

### AKG

Yes, that works.

3. Jan 9, 2007

### VinnyCee

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

4. Jan 10, 2007

### AKG

Yes, everything is right.