Joan is either a knight or a knave. Knights always tell the truth, and only the truth; knaves always tell falsehoods, and only falsehoods. Someone asks Joan, “Are you a knight?” She replies, “If I am a knight then I’ll eat my hat.” (a) Must Joan eat her hat? (b) Let’s set this up as problem in propositional logic. Introduce the following propositions: P = “Joan is a knight” Q = “Joan will eat her hat”. Translate what we’re given into propositional logic, i.e., re-write the premises in terms of these propositions. (c) Using proof by enumeration, prove that your answer from part (1) follows from the premises you wrote in part (2). (No inference rules allowed.)