Answer to Question #296693 in Discrete Mathematics for shahana

Question

Are these system specifications consistent? “The router

can send packets to the edge system only if it supports the

new address space. For the router to support the new ad-

dress space it is necessary that the latest software release

be installed. The router can send packets to the edge sys-

tem if the latest software release is installed, The router

does not support the new address space.”

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.