Answer to Question #296692 in Discrete Mathematics for shahana

Question

Are these system specifications consistent? “The system

is in multiuser state if and only if it is operating normally.

If the system is operating normally, the kernel is func-

tioning. The kernel is not functioning or the system is

in interrupt mode. If the system is not in multiuser state,

then it is in interrupt mode. The system is not in interrupt

mode.”

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.