In option A, P=TRUE.
Since we have P->Q and P-> R, Q and R both must be TRUE. (Modus ponens).
Now for the rule Q->R' as Q is TRUE, R' must be TRUE which means R should be FALSE. But we have already deduced R as TRUE.
So, This gives a contradiction. Hence A is inconsistent.
For option C, S and M both should be FALSE as S' and M' are part of the system. Now, to make R ∪ M as TRUE, the only option is R should be TRUE and To make R' ∪ S as TRUE, the only option is R' should be TRUE which means R should be FALSE giving us contradiction again!! Hence, C too is inconsistent.
For B, you can try assigning values you will not get a contradiction so its a consistent system.
So, the answer is B.
