A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, William, Aria, Elizabeth, Owen, and Lucas. "If Elizabeth is a knave then Aria is a knave," Sophia claimed. "Owen is a knight or Lucas is a knave," William declared. Aria commented, "Lucas is not a knight". Elizabeth said that Aria is not a knave. In Owen's words: "Sophia is a knave if and only if Sophia is a knight". "Owen is a knight and Lucas is a knight" - Lucas. So who is a knight and who is a knave?
Sophia is a knight, William is a knight, Aria is a knight, Elizabeth is a knight, Owen is a knave, and Lucas is a knave.
(1) Sophia is a knight
(2) William is a knight
(3) Aria is a knight
(4) Elizabeth is a knight
(5) Owen is a knave
(6) Lucas is a knave
Assume Sophia is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Aria is a knave. Assume Elizabeth is a knight. No contradiction is found in their claim that Aria is not a knave. Assume Aria is a knight. No contradiction is found in their claim that Lucas is not a knight. Lucas cannot be a knight, because this would contradict the claim of Aria that Lucas is not a knight. Assume Lucas is a knave. No contradiction is found in their false claim that Owen is a knight and Lucas is a knight. Owen cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight. Assume Owen is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight. Assume William is a knight. No contradiction is found in their claim that Owen is a knight or Lucas is a knave.