A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Abigail, Aria, Liam, Sebastian, and Scarlett. "Abigail is a knave or Scarlett is a knight," Chloe claimed. Abigail noted, "Liam is a knight". "Abigail is not a knave," Aria declared. Liam stated, "Sebastian is a knight or Chloe is a knight". Sebastian was heard saying, "Aria is a knave if and only if Scarlett is a knight". Scarlett expressed that Liam is not a knave. So who is a knight and who is a knave?
Chloe is a knight, Abigail is a knight, Aria is a knight, Liam is a knight, Sebastian is a knave, and Scarlett is a knight.
(1) Chloe is a knight
(2) Abigail is a knight
(3) Aria is a knight
(4) Liam is a knight
(5) Sebastian is a knave
(6) Scarlett is a knight
Assume Chloe is a knight. No contradiction is found in their claim that Abigail is a knave or Scarlett is a knight. Assume Abigail is a knight. No contradiction is found in their claim that Liam is a knight. Assume Liam is a knight. No contradiction is found in their claim that Sebastian is a knight or Chloe is a knight. Assume Sebastian is a knight. No contradiction is found in their claim that Aria is a knave if and only if Scarlett is a knight. Assume Aria is a knight. No contradiction is found in their claim that Abigail is not a knave. Scarlett cannot be a knight, because this would contradict the claim of Sebastian that Aria is a knave if and only if Scarlett is a knight. Scarlett cannot be a knave, because this would contradict the claim of Chloe that Abigail is a knave or Scarlett is a knight. We have exhausted all possibilities for Scarlett, so let us go back and reconsider Aria. Aria cannot be a knave, because this would contradict the false claim of their own that Abigail is not a knave. We have exhausted all possibilities for Aria, so let us go back and reconsider Sebastian. Assume Sebastian is a knave. No contradiction is found in their false claim that Aria is a knave if and only if Scarlett is a knight. Assume Aria is a knight. No contradiction is found in their claim that Abigail is not a knave. Assume Scarlett is a knight. No contradiction is found in their claim that Liam is not a knave.