A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Aurora, Aria, Lily, Abigail, Noah, and Emily. Aurora expressed that Emily is a knave. According to Aria, "Aurora is a knave if and only if Abigail is a knight". Lily said that Aurora is a knave and Aria is a knave. As Abigail put it, "If Emily is a knight then Aria is a knight". Noah said that Aurora is a knight or Emily is a knight. As Emily put it, "If Emily is a knight then Abigail is a knight". So who is a knight and who is a knave?
Aurora is a knave, Aria is a knight, Lily is a knave, Abigail is a knight, Noah is a knight, and Emily is a knight.
(1) Aurora is a knave
(2) Aria is a knight
(3) Lily is a knave
(4) Abigail is a knight
(5) Noah is a knight
(6) Emily is a knight
Assume Aurora is a knight. No contradiction is found in their claim that Emily is a knave. Emily cannot be a knight, because this would contradict the claim of Aurora that Emily is a knave. Emily cannot be a knave, because this would contradict the false claim of their own that If Emily is a knight then Abigail is a knight. We have exhausted all possibilities for Emily, so let us go back and reconsider Aurora. Assume Aurora is a knave. No contradiction is found in their false claim that Emily is a knave. Assume Emily is a knight. No contradiction is found in their claim that If Emily is a knight then Abigail is a knight. Assume Abigail is a knight. No contradiction is found in their claim that If Emily is a knight then Aria is a knight. Assume Aria is a knight. No contradiction is found in their claim that Aurora is a knave if and only if Abigail is a knight. Lily cannot be a knight, because this would contradict the claim of their own that Aurora is a knave and Aria is a knave. Assume Lily is a knave. No contradiction is found in their false claim that Aurora is a knave and Aria is a knave. Assume Noah is a knight. No contradiction is found in their claim that Aurora is a knight or Emily is a knight.