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