A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Oliver, Emily, Henry, David, and Lucas. Chloe commented, "Oliver is a knave or Emily is a knight". As Oliver put it, "David is a knight or Emily is a knave". In a statement by Emily: "Emily is a knight or Lucas is a knave". Henry told you that David is a knight if and only if Oliver is a knave. As David put it, "Henry is a knave and Emily is a knight". Lucas noted, "Emily is a knight or Oliver is a knave". So who is a knight and who is a knave?
Chloe is a knight, Oliver is a knight, Emily is a knight, Henry is a knave, David is a knight, and Lucas is a knight.
(1) Chloe is a knight
(2) Oliver is a knight
(3) Emily is a knight
(4) Henry is a knave
(5) David is a knight
(6) Lucas is a knight
Assume Chloe is a knight. No contradiction is found in their claim that Oliver is a knave or Emily is a knight. Assume Oliver is a knight. No contradiction is found in their claim that David is a knight or Emily is a knave. Assume David is a knight. No contradiction is found in their claim that Henry is a knave and Emily is a knight. Henry cannot be a knight, because this would contradict the claim of their own that David is a knight if and only if Oliver is a knave. Assume Henry is a knave. No contradiction is found in their false claim that David is a knight if and only if Oliver is a knave. Assume Emily is a knight. No contradiction is found in their claim that Emily is a knight or Lucas is a knave. Assume Lucas is a knight. No contradiction is found in their claim that Emily is a knight or Oliver is a knave.