We say that a set of system specifications is consistent if there is a way for all the specifications to be simultaneously true. Otherwise, the set of specifications is inconsistent. Consider the following set of system specifications:

If the kernel is functioning, then the system is not in interrupt mode.

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

If the system is in interrupt mode, then the system is in multiuser state.

The kernel is functioning or the system is not operating normally.

The system is in interrupt mode.

Use propositional logic to determine if the set of system specifications consistent or inconsistent by doing the following:

Part a $(1$ pts$)$ : First, define the appropriate propositional variables for representing the system specifications.

Part b $(2$ pts$)$ : Then, translate each of the system specifications into propositional logic using the propositional variables you defined in part a$.$

Part c $(2$ pts$)$ : Finally, is the set of system specifications consistent or inconsistent? Justify your answer.