A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, Elizabeth, Aria, Amelia, Liam, and Sophia. Emma noted, "If Aria is a knight then Emma is a knight". Elizabeth said, "Emma is not a knight." Aria said, "Amelia is not a knight." According to Amelia, "If Liam is a knight then Sophia is a knave". "If Aria is a knave then Elizabeth is a knave," Liam mentioned. In a statement by Sophia: "Elizabeth is a knave and Emma is a knight". So who is a knight and who is a knave?
Emma is a knight, Elizabeth is a knave, Aria is a knight, Amelia is a knave, Liam is a knight, and Sophia is a knight.
(1) Emma is a knight
(2) Elizabeth is a knave
(3) Aria is a knight
(4) Amelia is a knave
(5) Liam is a knight
(6) Sophia is a knight
Assume Emma is a knight. No contradiction is found in their claim that If Aria is a knight then Emma is a knight. Assume Aria is a knight. No contradiction is found in their claim that Amelia is not a knight. Amelia cannot be a knight, because this would contradict the claim of Aria that Amelia is not a knight. Assume Amelia is a knave. No contradiction is found in their false claim that If Liam is a knight then Sophia is a knave. Assume Liam is a knight. No contradiction is found in their claim that If Aria is a knave then Elizabeth is a knave. Elizabeth cannot be a knight, because this would contradict the claim of their own that Emma is not a knight. Assume Elizabeth is a knave. No contradiction is found in their false claim that Emma is not a knight. Assume Sophia is a knight. No contradiction is found in their claim that Elizabeth is a knave and Emma is a knight.