A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: David, William, Mia, Chloe, Owen, and Isabella. "Mia is not a knight" - David. "Mia is a knave if and only if Isabella is a knight" - William. "David is a knight or Owen is a knave" - Mia. Chloe was heard saying, "David is not a knave". Owen noted, "Isabella is a knave or William is a knight". "David is a knave," Isabella declared. So who is a knight and who is a knave?
David is a knave, William is a knave, Mia is a knight, Chloe is a knave, Owen is a knave, and Isabella is a knight.
(1) David is a knave
(2) William is a knave
(3) Mia is a knight
(4) Chloe is a knave
(5) Owen is a knave
(6) Isabella is a knight
Assume David is a knight. No contradiction is found in their claim that Mia is not a knight. Mia cannot be a knight, because this would contradict the claim of David that Mia is not a knight. Mia cannot be a knave, because this would contradict the false claim of their own that David is a knight or Owen is a knave. We have exhausted all possibilities for Mia, so let us go back and reconsider David. Assume David is a knave. No contradiction is found in their false claim that Mia is not a knight. Assume Mia is a knight. No contradiction is found in their claim that David is a knight or Owen is a knave. Owen cannot be a knight, because this would contradict the claim of Mia that David is a knight or Owen is a knave. Assume Owen is a knave. No contradiction is found in their false claim that Isabella is a knave or William is a knight. Assume Isabella is a knight. No contradiction is found in their claim that David is a knave. William cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Isabella is a knight. Assume William is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Isabella is a knight. Chloe cannot be a knight, because this would contradict the claim of their own that David is not a knave. Assume Chloe is a knave. No contradiction is found in their false claim that David is not a knave.