Make your own key to translate into propositional logic the portions of the following argument. Using a direct proof, prove that the resulting argument is valid. Inspector Tarski told his assistant, Mr. Carroll, If Wittgenstein had mud on his boots, then he was in the field. Furthermore, if Wittgenstein was in the field, then he is the prime suspect for the murder of Dodgson. Wittgenstein did have mud on his boots. We conclude, Wittgenstein is the prime suspect for the murder of Dodgson.