A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Joseph, Amelia, William, Lily, and Ethan. In a statement by Abigail: "If Ethan is a knave then Joseph is a knave". "Amelia is a knave if and only if William is a knight" - Joseph. Amelia remarked, "Lily is not a knight". As William put it, "Amelia is a knave or Amelia is a knight". Lily commented, "Abigail is a knight if and only if Lily is a knight". Ethan asserted: "Joseph is a knave". So who is a knight and who is a knave?
Abigail is a knight, Joseph is a knave, Amelia is a knight, William is a knight, Lily is a knave, and Ethan is a knight.
(1) Abigail is a knight
(2) Joseph is a knave
(3) Amelia is a knight
(4) William is a knight
(5) Lily is a knave
(6) Ethan is a knight
Assume Abigail is a knight. No contradiction is found in their claim that If Ethan is a knave then Joseph is a knave. Assume Ethan is a knight. No contradiction is found in their claim that Joseph is a knave. Joseph cannot be a knight, because this would contradict the claim of Ethan that Joseph is a knave. Assume Joseph is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if William is a knight. Assume Amelia is a knight. No contradiction is found in their claim that Lily is not a knight. Lily cannot be a knight, because this would contradict the claim of Amelia that Lily is not a knight. Assume Lily is a knave. No contradiction is found in their false claim that Abigail is a knight if and only if Lily is a knight. Assume William is a knight. No contradiction is found in their claim that Amelia is a knave or Amelia is a knight.