A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Sophia, Chloe, Michael, Jackson, and Grace. As Aurora put it, "If Jackson is a knave then Chloe is a knight". Sophia expressed that Chloe is a knave. Chloe noted, "Michael is a knave if and only if Jackson is a knight". "Aurora is a knight," Michael mentioned. "Chloe is a knight or Sophia is a knave," Jackson declared. Grace commented, "Chloe is not a knave". So who is a knight and who is a knave?
Aurora is a knave, Sophia is a knight, Chloe is a knave, Michael is a knave, Jackson is a knave, and Grace is a knave.
(1) Aurora is a knave
(2) Sophia is a knight
(3) Chloe is a knave
(4) Michael is a knave
(5) Jackson is a knave
(6) Grace is a knave
Assume Aurora is a knight. No contradiction is found in their claim that If Jackson is a knave then Chloe is a knight. Assume Jackson is a knight. No contradiction is found in their claim that Chloe is a knight or Sophia is a knave. Assume Chloe is a knight. No contradiction is found in their claim that Michael is a knave if and only if Jackson is a knight. Michael cannot be a knight, because this would contradict the claim of Chloe that Michael is a knave if and only if Jackson is a knight. Michael cannot be a knave, because this would contradict the false claim of their own that Aurora is a knight. We have exhausted all possibilities for Michael, so let us go back and reconsider Chloe. Assume Chloe is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Jackson is a knight. Assume Michael is a knight. No contradiction is found in their claim that Aurora is a knight. Sophia cannot be a knight, because this would contradict the claim of Jackson that Chloe is a knight or Sophia is a knave. Sophia cannot be a knave, because this would contradict the false claim of their own that Chloe is a knave. We have exhausted all possibilities for Sophia, so let us go back and reconsider Michael. Michael cannot be a knave, because this would contradict the false claim of Chloe that Michael is a knave if and only if Jackson is a knight. We have exhausted all possibilities for Michael and Chloe, so let us go back and reconsider Jackson. Assume Jackson is a knave. No contradiction is found in their false claim that Chloe is a knight or Sophia is a knave. Chloe cannot be a knight, because this would contradict the false claim of Jackson that Chloe is a knight or Sophia is a knave. Chloe cannot be a knave, because this would contradict the claim of Aurora that If Jackson is a knave then Chloe is a knight. We have exhausted all possibilities for Chloe and Jackson, so let us go back and reconsider Aurora. Assume Aurora is a knave. No contradiction is found in their false claim that If Jackson is a knave then Chloe is a knight. Jackson cannot be a knight, because this would contradict the false claim of Aurora that If Jackson is a knave then Chloe is a knight. Assume Jackson is a knave. No contradiction is found in their false claim that Chloe is a knight or Sophia is a knave. Chloe cannot be a knight, because this would contradict the false claim of Aurora that If Jackson is a knave then Chloe is a knight. Assume Chloe is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Jackson is a knight. Michael cannot be a knight, because this would contradict the false claim of Chloe that Michael is a knave if and only if Jackson is a knight. Assume Michael is a knave. No contradiction is found in their false claim that Aurora is a knight. Assume Sophia is a knight. No contradiction is found in their claim that Chloe is a knave. Grace cannot be a knight, because this would contradict the claim of their own that Chloe is not a knave. Assume Grace is a knave. No contradiction is found in their false claim that Chloe is not a knave.