Ignore Part A, please just solve Part B and C.

In this problem, we will use the fastest method, prove5, to solve some word problems which can be encoded as problems in propositional logic. For each, give the encoding of the statements in the problem as symbols. (You might want to review pp.32-33 in the textbook before starting.) Part A Do problem 2.10 from your textbook. Part B A man and a woman are talking. "I am a man" said the person with black hair. "I am a woman" said the person with white hair. At least one of them is Iying. Formalize the puzzle using propositional logic and show using resolution that both of them are lying. Part C Three boxes are presented to you. One contains gold, the other two are empty. Each box has imprinted on it a clue as to its contents; the clues are: - Box 1 "The gold is not here" - Box 2 "The gold is not here" - Box 3 "The gold is in Box 2" Only one message is true; the other two are false. Which box has the gold? Formalize the puzzle using propositional logic and find the solution using resolution