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: Penelope, Emily, and David. "If Penelope is a knight then David is a knight" - Penelope. "Emily is a knight if and only if Penelope is a knight" - Emily. "Emily is not a knight," David mentioned. 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 Penelope is a knight.  No contradiction is found in their claim that If Penelope is a knight then David is a knight.
 Assume David is a knight.  No contradiction is found in their claim that Emily is not a knight.
 Emily cannot be a knight, because this would contradict the claim of David that Emily is not a knight.
 Assume Emily is a knave.  No contradiction is found in their false claim that Emily is a knight if and only if Penelope is a knight.
 Therefore, (1) Penelope is a knight
 (2) Emily is a knave
 (3) David is a knight
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: Penelope, Emily, and David. "If Penelope is a knight then David is a knight" - Penelope. "Emily is a knight if and only if Penelope is a knight" - Emily. "Emily is not a knight," David mentioned. 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 Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then David is a knight.
Assume David is a knight. No contradiction is found in their claim that Emily is not a knight.
Emily cannot be a knight, because this would contradict the claim of David that Emily is not a knight.
Assume Emily is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Penelope is a knight.
Therefore, (1) Penelope is a knight
(2) Emily is a knave
(3) David is a knight </think>
<answer> (1) Penelope is a knight
(2) Emily is a knave
(3) David is a knight </answer>
Penelope Emily David
(1) Penelope is a knight
(2) Emily is a knave
(3) David is a knight
(('->', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 1)))
rule