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: Jacob, Oliver, and Emma. "Emma is a knave or Jacob is a knight," Jacob claimed. Oliver expressed that Jacob is a knave and Emma is a knave. "Oliver is a knight and Jacob is a knave" - Emma. 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 Jacob is a knight.  No contradiction is found in their claim that Emma is a knave or Jacob is a knight.
 Emma cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Jacob is a knave.
 Assume Emma is a knave.  No contradiction is found in their false claim that Oliver is a knight and Jacob is a knave.
 Oliver cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Emma is a knave.
 Assume Oliver is a knave.  No contradiction is found in their false claim that Jacob is a knave and Emma is a knave.
 Therefore, (1) Jacob is a knight
 (2) Oliver is a knave
 (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: Jacob, Oliver, and Emma. "Emma is a knave or Jacob is a knight," Jacob claimed. Oliver expressed that Jacob is a knave and Emma is a knave. "Oliver is a knight and Jacob is a knave" - Emma. 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 Jacob is a knight. No contradiction is found in their claim that Emma is a knave or Jacob is a knight.
Emma cannot be a knight, because this would contradict the claim of their own that Oliver is a knight and Jacob is a knave.
Assume Emma is a knave. No contradiction is found in their false claim that Oliver is a knight and Jacob is a knave.
Oliver cannot be a knight, because this would contradict the claim of their own that Jacob is a knave and Emma is a knave.
Assume Oliver is a knave. No contradiction is found in their false claim that Jacob is a knave and Emma is a knave.
Therefore, (1) Jacob is a knight
(2) Oliver is a knave
(3) Emma is a knave </think>
<answer> (1) Jacob is a knight
(2) Oliver is a knave
(3) Emma is a knave </answer>
Jacob Oliver Emma
(1) Jacob is a knight
(2) Oliver is a knave
(3) Emma is a knave
(('or', ('lying', 2), ('telling-truth', 0)), ('and', ('lying', 0), ('lying', 2)), ('and', ('telling-truth', 1), ('lying', 0)))
rule