A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: James, Logan, Isabella, Liam, Aria, and Victoria. James said that If Isabella is a knave then Logan is a knave. "Liam is a knave or Isabella is a knave," Logan claimed. Isabella said that Liam is a knight if and only if James is a knight. As Liam put it, "James is a knight if and only if Aria is a knave". "Liam is not a knight" - Aria. In a statement by Victoria: "Aria is a knave and Liam is a knight". So who is a knight and who is a knave?
James is a knight, Logan is a knave, Isabella is a knight, Liam is a knight, Aria is a knave, and Victoria is a knight.
(1) James is a knight
(2) Logan is a knave
(3) Isabella is a knight
(4) Liam is a knight
(5) Aria is a knave
(6) Victoria is a knight
Assume James is a knight. No contradiction is found in their claim that If Isabella is a knave then Logan is a knave. Assume Isabella is a knight. No contradiction is found in their claim that Liam is a knight if and only if James is a knight. Assume Liam is a knight. No contradiction is found in their claim that James is a knight if and only if Aria is a knave. Aria cannot be a knight, because this would contradict the claim of Liam that James is a knight if and only if Aria is a knave. Assume Aria is a knave. No contradiction is found in their false claim that Liam is not a knight. Logan cannot be a knight, because this would contradict the claim of their own that Liam is a knave or Isabella is a knave. Assume Logan is a knave. No contradiction is found in their false claim that Liam is a knave or Isabella is a knave. Assume Victoria is a knight. No contradiction is found in their claim that Aria is a knave and Liam is a knight.