1a) There are three islanders: A says If B and I are both telling the truth, then so is C, B says If C is telling the truth, then A is lying, and C says It is not the case that all three of us are telling the truth. Using propositional variables a, b, and c to represent the truth of the statements of A, B, and C respectively, we can represent the problem by the three premises a ((a b) c), b (c a), and c (a b c). Determine the conclusion as a conjunction of three literals, and give a deductive sequence proof of this conclusion from the premises.

1b) For each of the three islanders, either derive a contradiction from the assumption they are telling the truth, or derive a contradiction from the assumption that they are lying. (If you can only answer one, please answer the first part) Thank you.