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: Aurora, Jackson, and Emma. Aurora was heard saying, "Jackson is not a knight". Jackson commented, "Emma is not a knight". Emma said that Jackson is a knight if and only if Emma is a knight. 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 Aurora is a knight.  No contradiction is found in their claim that Jackson is not a knight.
 Jackson cannot be a knight, because this would contradict the claim of Aurora that Jackson is not a knight.
 Assume Jackson is a knave.  No contradiction is found in their false claim that Emma is not a knight.
 Emma cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Emma is a knight.
 Emma cannot be a knave, because this would contradict the false claim of Jackson that Emma is not a knight.
 We have exhausted all possibilities for Emma and Jackson, so let us go back and reconsider Aurora.
 Assume Aurora is a knave.  No contradiction is found in their false claim that Jackson is not a knight.
 Assume Jackson is a knight.  No contradiction is found in their claim that Emma is not a knight.
 Emma cannot be a knight, because this would contradict the claim of Jackson that Emma is not a knight.
 Assume Emma is a knave.  No contradiction is found in their false claim that Jackson is a knight if and only if Emma is a knight.
 Therefore, (1) Aurora is a knave
 (2) Jackson is a knight
 (3) Emma 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: Aurora, Jackson, and Emma. Aurora was heard saying, "Jackson is not a knight". Jackson commented, "Emma is not a knight". Emma said that Jackson is a knight if and only if Emma is a knight. 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 Aurora is a knight. No contradiction is found in their claim that Jackson is not a knight.
Jackson cannot be a knight, because this would contradict the claim of Aurora that Jackson is not a knight.
Assume Jackson is a knave. No contradiction is found in their false claim that Emma is not a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Emma is a knight.
Emma cannot be a knave, because this would contradict the false claim of Jackson that Emma is not a knight.
We have exhausted all possibilities for Emma and Jackson, so let us go back and reconsider Aurora.
Assume Aurora is a knave. No contradiction is found in their false claim that Jackson is not a knight.
Assume Jackson is a knight. No contradiction is found in their claim that Emma is not a knight.
Emma cannot be a knight, because this would contradict the claim of Jackson that Emma is not a knight.
Assume Emma is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Emma is a knight.
Therefore, (1) Aurora is a knave
(2) Jackson is a knight
(3) Emma is a knave </think>
<answer> (1) Aurora is a knave
(2) Jackson is a knight
(3) Emma is a knave </answer>
Aurora Jackson Emma
(1) Aurora is a knave
(2) Jackson is a knight
(3) Emma is a knave
(('not', ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 2)))
rule