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: Evelyn, Michael, and William. Evelyn said, "If Michael is a knave then Evelyn is a knight." Michael noted, "Evelyn is a knave or Evelyn is a knight". "Evelyn is a knight if and only if Michael is a knave" - William. 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 Evelyn is a knight.  No contradiction is found in their claim that If Michael is a knave then Evelyn is a knight.
 Assume Michael is a knight.  No contradiction is found in their claim that Evelyn is a knave or Evelyn is a knight.
 William cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Michael is a knave.
 Assume William is a knave.  No contradiction is found in their false claim that Evelyn is a knight if and only if Michael is a knave.
 Therefore, (1) Evelyn is a knight
 (2) Michael is a knight
 (3) William 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: Evelyn, Michael, and William. Evelyn said, "If Michael is a knave then Evelyn is a knight." Michael noted, "Evelyn is a knave or Evelyn is a knight". "Evelyn is a knight if and only if Michael is a knave" - William. 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 Evelyn is a knight. No contradiction is found in their claim that If Michael is a knave then Evelyn is a knight.
Assume Michael is a knight. No contradiction is found in their claim that Evelyn is a knave or Evelyn is a knight.
William cannot be a knight, because this would contradict the claim of their own that Evelyn is a knight if and only if Michael is a knave.
Assume William is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Michael is a knave.
Therefore, (1) Evelyn is a knight
(2) Michael is a knight
(3) William is a knave </think>
<answer> (1) Evelyn is a knight
(2) Michael is a knight
(3) William is a knave </answer>
Evelyn Michael William
(1) Evelyn is a knight
(2) Michael is a knight
(3) William is a knave
(('->', ('lying', 1), ('telling-truth', 0)), ('or', ('lying', 0), ('telling-truth', 0)), ('<=>', ('telling-truth', 0), ('lying', 1)))
rule