A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Matthew, Abigail, Elizabeth, Daniel, Lucas, and Aria. In Matthew's words: "If Aria is a knight then Lucas is a knave". Abigail remarked, "Elizabeth is a knave if and only if Matthew is a knight". Elizabeth asserted: "Matthew is not a knight". Daniel told you that Lucas is a knave or Abigail is a knight. Lucas said, "Matthew is a knight and Lucas is a knight." According to Aria, "Daniel is a knight if and only if Elizabeth is a knave". So who is a knight and who is a knave?
Matthew is a knight, Abigail is a knight, Elizabeth is a knave, Daniel is a knight, Lucas is a knave, and Aria is a knight.
(1) Matthew is a knight
(2) Abigail is a knight
(3) Elizabeth is a knave
(4) Daniel is a knight
(5) Lucas is a knave
(6) Aria is a knight
Assume Matthew is a knight. No contradiction is found in their claim that If Aria is a knight then Lucas is a knave. Assume Aria is a knight. No contradiction is found in their claim that Daniel is a knight if and only if Elizabeth is a knave. Assume Daniel is a knight. No contradiction is found in their claim that Lucas is a knave or Abigail is a knight. Lucas cannot be a knight, because this would contradict the claim of Matthew that If Aria is a knight then Lucas is a knave. Assume Lucas is a knave. No contradiction is found in their false claim that Matthew is a knight and Lucas is a knight. Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knave if and only if Matthew is a knight. Elizabeth cannot be a knight, because this would contradict the claim of Abigail that Elizabeth is a knave if and only if Matthew is a knight. Assume Elizabeth is a knave. No contradiction is found in their false claim that Matthew is not a knight.