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: Elizabeth, Ava, and David. According to Elizabeth, "Elizabeth is a knight if and only if David is a knight". As Ava put it, "Ava is a knight if and only if Elizabeth is a knave". David expressed that Ava is a knave if and only if Elizabeth is a knave. 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 Elizabeth is a knight.  No contradiction is found in their claim that Elizabeth is a knight if and only if David is a knight.
 Assume David is a knight.  No contradiction is found in their claim that Ava is a knave if and only if Elizabeth is a knave.
 Ava cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Elizabeth is a knave.
 Ava cannot be a knave, because this would contradict the false claim of their own that Ava is a knight if and only if Elizabeth is a knave.
 We have exhausted all possibilities for Ava, so let us go back and reconsider David.
 David cannot be a knave, because this would contradict the claim of Elizabeth that Elizabeth is a knight if and only if David is a knight.
 We have exhausted all possibilities for David, so let us go back and reconsider Elizabeth.
 Assume Elizabeth is a knave.  No contradiction is found in their false claim that Elizabeth is a knight if and only if David is a knight.
 Assume David is a knight.  No contradiction is found in their claim that Ava is a knave if and only if Elizabeth is a knave.
 Ava cannot be a knight, because this would contradict the claim of David that Ava is a knave if and only if Elizabeth is a knave.
 Assume Ava is a knave.  No contradiction is found in their false claim that Ava is a knight if and only if Elizabeth is a knave.
 Therefore, (1) Elizabeth is a knave
 (2) Ava 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: Elizabeth, Ava, and David. According to Elizabeth, "Elizabeth is a knight if and only if David is a knight". As Ava put it, "Ava is a knight if and only if Elizabeth is a knave". David expressed that Ava is a knave if and only if Elizabeth is a knave. 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 Elizabeth is a knight. No contradiction is found in their claim that Elizabeth is a knight if and only if David is a knight.
Assume David is a knight. No contradiction is found in their claim that Ava is a knave if and only if Elizabeth is a knave.
Ava cannot be a knight, because this would contradict the claim of their own that Ava is a knight if and only if Elizabeth is a knave.
Ava cannot be a knave, because this would contradict the false claim of their own that Ava is a knight if and only if Elizabeth is a knave.
We have exhausted all possibilities for Ava, so let us go back and reconsider David.
David cannot be a knave, because this would contradict the claim of Elizabeth that Elizabeth is a knight if and only if David is a knight.
We have exhausted all possibilities for David, so let us go back and reconsider Elizabeth.
Assume Elizabeth is a knave. No contradiction is found in their false claim that Elizabeth is a knight if and only if David is a knight.
Assume David is a knight. No contradiction is found in their claim that Ava is a knave if and only if Elizabeth is a knave.
Ava cannot be a knight, because this would contradict the claim of David that Ava is a knave if and only if Elizabeth is a knave.
Assume Ava is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Elizabeth is a knave.
Therefore, (1) Elizabeth is a knave
(2) Ava is a knave
(3) David is a knight </think>
<answer> (1) Elizabeth is a knave
(2) Ava is a knave
(3) David is a knight </answer>
Elizabeth Ava David
(1) Elizabeth is a knave
(2) Ava is a knave
(3) David is a knight
(('<=>', ('telling-truth', 0), ('telling-truth', 2)), ('<=>', ('telling-truth', 1), ('lying', 0)), ('<=>', ('lying', 1), ('lying', 0)))
rule