A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aiden, David, and Abigail. Aiden told you that Abigail is a knave. David told you that Aiden is a knave or Abigail is a knave. "David is a knight if and only if David is a knave" - Abigail. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
user
Assume Aiden is a knight.  No contradiction is found in their claim that Abigail is a knave.
 Abigail cannot be a knight, because this would contradict the claim of Aiden that Abigail is a knave.
 Assume Abigail is a knave.  No contradiction is found in their false claim that David is a knight if and only if David is a knave.
 Assume David is a knight.  No contradiction is found in their claim that Aiden is a knave or Abigail is a knave.
 Therefore, (1) Aiden is a knight
 (2) David is a knight
 (3) Abigail is a knave
A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 3 inhabitants: Aiden, David, and Abigail. Aiden told you that Abigail is a knave. David told you that Aiden is a knave or Abigail is a knave. "David is a knight if and only if David is a knave" - Abigail. So who is a knight and who is a knave? Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags, for example <answer> (1) Zoey is a knight
(2) Oliver is a knight
(3)... </answer>.
Assistant: Let me solve this step by step.
<think> 
Assume Aiden is a knight. No contradiction is found in their claim that Abigail is a knave.
Abigail cannot be a knight, because this would contradict the claim of Aiden that Abigail is a knave.
Assume Abigail is a knave. No contradiction is found in their false claim that David is a knight if and only if David is a knave.
Assume David is a knight. No contradiction is found in their claim that Aiden is a knave or Abigail is a knave.
Therefore, (1) Aiden is a knight
(2) David is a knight
(3) Abigail is a knave </think>
<answer> (1) Aiden is a knight
(2) David is a knight
(3) Abigail is a knave </answer>
Aiden David Abigail
(1) Aiden is a knight
(2) David is a knight
(3) Abigail is a knave
(('lying', 2), ('or', ('lying', 0), ('lying', 2)), ('<=>', ('telling-truth', 1), ('lying', 1)))
rule