Answer to Question #296694 in Discrete Mathematics for shahana

Question

Are these system specifications consistent? “If the file

system is not locked, then new messages will be queued.

If the file system is not locked, then the system is func-

tioning normally, and conversely. If new messages are not

queued, then they will be sent to the message buffer. If

the file system is not locked, then new messages will be

sent to the message buffer. New messages will not be sent

to the message buffer.”

Answer 1

Consider,

P: System is on multi-user state

Q : System is operating normally

R: The kernel is functioning

S: System is in interrupt mode

Then We will get following Prepositional Formula,

1) The system is in multi-user state if and only if it is operating normally. ( P <--> Q)

2) If the system is operating normally, the kernel is functioning. (Q --> R)

3) The kernel is not functioning or the system is in interrupt mode. (~R V S)

4) If the system is not in multi-user state, then it is in interrupt mode. (~P --> S)

5) The system is not in interrupt mode (~S)

Now,

In (5), We have to take S = F, then and only then we get (5) as True. 

In (3), We have taken S = F, then we have to take (R = F) then and only then we will get (3) as True.

In(4), Since S = F, then we have to take (P = T), then and only then we will get (4) as True.

In(2), Since R = F, then we have to take (Q = F), then and only then we will get (2) as True.

In(1), we have P = T and Q = F, which can never generate a true value, (1) will be false.

Hence this System is not Consistent.