Final answer:
The argument is formalized using symbolic logic, with M, O, K, and I representing different states of the system. The conclusion that the system is not in interrupt mode (¬I) logically follows from the premises, making the argument valid.
Step-by-step explanation:
To formalize the given arguments, we will start by assigning the following symbolic representations to the statements:
- M stands for 'The system is in a multi-user state.'
- O stands for 'The system is operating normally.'
- K stands for 'The kernel is functioning.'
- I stands for 'The system is in interrupt mode.'
The original statements can now be formalized as follows:
- M ↔ O (The system is in a multi-user state if and only if it is operating normally.)
- O → K (If the system is operating normally, the kernel is functioning.)
- ¬K ∨ I (Either the kernel is not functioning or the system is in interrupt mode.)
- ¬M → I (If the system is not in multi-user state, then it is in interrupt mode.)
From the propositions given, we can check the validity of the conclusion that the system is not in interrupt mode (¬I).
To verify the validity of the argument, we will determine if the conclusion ¬I necessarily follows from the premises. Here, we can use a method such as truth tables or rules of inference to determine if the argument is valid.
Starting with the first premise M ↔ O, we know if M is true, then O must be true and vice-versa. Since O → K, if O is true, K must also be true. Given that ¬K ∨ I, but we already know from the previous premises that K is true, I must be false to satisfy this disjunction—hence the system cannot be in interrupt mode. Furthermore, since ¬M → I and we concluded I is false, M must be true to make this conditional true. Therefore, the argument is valid because the conclusion logically follows from the premises.