A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Lily, Aiden, Ava, Jacob, Logan, and Elizabeth. In Lily's words: "Ava is not a knave". "Logan is a knight or Logan is a knave," Aiden claimed. Ava told you that Lily is a knave if and only if Jacob is a knave. "Lily is a knave if and only if Aiden is a knave," Jacob declared. Logan said, "Lily is a knight or Jacob is a knave." As Elizabeth put it, "Jacob is a knave or Aiden is a knave". So who is a knight and who is a knave?
Lily is a knight, Aiden is a knight, Ava is a knight, Jacob is a knight, Logan is a knight, and Elizabeth is a knave.
(1) Lily is a knight
(2) Aiden is a knight
(3) Ava is a knight
(4) Jacob is a knight
(5) Logan is a knight
(6) Elizabeth is a knave
Assume Lily is a knight. No contradiction is found in their claim that Ava is not a knave. Assume Ava is a knight. No contradiction is found in their claim that Lily is a knave if and only if Jacob is a knave. Assume Jacob is a knight. No contradiction is found in their claim that Lily is a knave if and only if Aiden is a knave. Assume Aiden is a knight. No contradiction is found in their claim that Logan is a knight or Logan is a knave. Assume Logan is a knight. No contradiction is found in their claim that Lily is a knight or Jacob is a knave. Elizabeth cannot be a knight, because this would contradict the claim of their own that Jacob is a knave or Aiden is a knave. Assume Elizabeth is a knave. No contradiction is found in their false claim that Jacob is a knave or Aiden is a knave.