Problem 2. A set of propositions is consistent if there is an assignment of trut

Question

Problem 2. A set of propositions is consistent if there is an assignment of truth values to each of the variables in the propositions that makes each proposition true. Is the following set of propositions consistent? The system is in multiuser state if and only if it is operating normally. If the system is operating normally, the kernel is functioning. 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 in interrupt mode.

Explanation / Answer

Here Consider,

M : System is in MutiUser State

N: System Operates Normally.

P: Kernal is functioning

I : System is in interrupt Mode.

From given

The prepostions will be as

M <=> N i.e, System is in mutluser state if and only if it is Operating Normally.

N - > P i.e. System Operating Normally, the kernel is functioning.

¬P I i.e., The kernal is not functioning or the system is in interrupt mode.

¬M -> I i.e., The kernal is not in multiUser state, then it is in interrupt Mode.

I i.e., The system is in Interrupt Mode.

Using M,N,P , and I as the atomic propositions, there are three rows of the truth table that have all ve of the above propositions true: the rows TTTT, FFTT, FFFT for M,N,P,I . Any one of these three choices for T/F assignment to M,N,P,I would do to show the above set is consistent.

M N P I M <=> N N -> P ¬P I ¬M -> I I F F F F T T T F F F F F T T T T T T F F T F T T F F F F F T T T T T T T F T F F F F T F F F T F T F F T T T F T T F F T F F F F T T T F T T T T T F F F F T T F F T F F T F T T T T T F T F F T F F F T F T T F T T T T T T F F T F T F F T T F T T F T T T T T T F T T F F F T T T T T T T T T

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