Are the following arguments valid or not? Use resolution or resolution refutation to find out.

1). If Kevin loses his disc or his AI system cannot be turned off, Kevin is trapped on the grid. If AI system has no off switch, it cannot be turned off. Kevin does not lose his disk. AI system has no off switch. Therefore, Kevin is trapped on the grid.

2). Anne goes to the library on Saturday or on Sunday. John also goes to the library on Saturday or Sunday. Therefore, both Anne and John will be at the library on Saturday, or both of them will be at the library on Sunday.

3). If the AI lecture is boring, I will fall asleep. If I fall asleep, I will hit my head on the desk. If I hit my head on the desk, I will go to the hospital. I did not go to the hospital. Therefore, the AI lecture is not boring.

4). When Prof. P. gets angry, he fails his entire class. When the entire class fails, the Chancellor gets complaints. When the Chancellor gets complaints, he will either fire Prof. P., cut his salary, or do both. Prof. P. got angry, and he was not fired. Therefore Prof. P.'s salary was cut.

Hint: follow the following steps to solve those problems

a) Extract the propositions from the argument and name them with single letter; b) Translate each sentence in the argument to either a hypothesis or a conclusion in propositional calculus;

c) Convert these expressions into CNF;

d) List the steps of the resolution (refutation) and state whether the argument is valid or not.