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