Question

1. 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.

2. Consider the islander problem. 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.

Answer 1