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)
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.