A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Elizabeth, Harper, Aria, Michael, and Alexander. "Alexander is a knave if and only if Harper is a knave," Emily declared. Elizabeth commented, "Michael is a knight or Aria is a knave". In a statement by Harper: "Emily is a knave or Elizabeth is a knight". Aria remarked, "Emily is a knight if and only if Michael is a knight". Michael told you that If Emily is a knave then Aria is a knave. Alexander asserted: "Harper is a knight and Michael is a knave". So who is a knight and who is a knave?
Emily is a knave, Elizabeth is a knight, Harper is a knight, Aria is a knave, Michael is a knight, and Alexander is a knave.
(1) Emily is a knave
(2) Elizabeth is a knight
(3) Harper is a knight
(4) Aria is a knave
(5) Michael is a knight
(6) Alexander is a knave
Assume Emily is a knight. No contradiction is found in their claim that Alexander is a knave if and only if Harper is a knave. Assume Alexander is a knight. No contradiction is found in their claim that Harper is a knight and Michael is a knave. Assume Harper is a knight. No contradiction is found in their claim that Emily is a knave or Elizabeth is a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight or Aria is a knave. Michael cannot be a knight, because this would contradict the claim of Alexander that Harper is a knight and Michael is a knave. Michael cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Aria is a knave. We have exhausted all possibilities for Michael, so let us go back and reconsider Elizabeth. Elizabeth cannot be a knave, because this would contradict the claim of Harper that Emily is a knave or Elizabeth is a knight. We have exhausted all possibilities for Elizabeth, so let us go back and reconsider Harper. Harper cannot be a knave, because this would contradict the claim of Emily that Alexander is a knave if and only if Harper is a knave. We have exhausted all possibilities for Harper, so let us go back and reconsider Alexander. Assume Alexander is a knave. No contradiction is found in their false claim that Harper is a knight and Michael is a knave. Harper cannot be a knight, because this would contradict the claim of Emily that Alexander is a knave if and only if Harper is a knave. Assume Harper is a knave. No contradiction is found in their false claim that Emily is a knave or Elizabeth is a knight. Elizabeth cannot be a knight, because this would contradict the false claim of Harper that Emily is a knave or Elizabeth is a knight. Assume Elizabeth is a knave. No contradiction is found in their false claim that Michael is a knight or Aria is a knave. Michael cannot be a knight, because this would contradict the false claim of Elizabeth that Michael is a knight or Aria is a knave. Michael cannot be a knave, because this would contradict the false claim of their own that If Emily is a knave then Aria is a knave. We have exhausted all possibilities for Michael, Elizabeth, Harper, and Alexander, so let us go back and reconsider Emily. Assume Emily is a knave. No contradiction is found in their false claim that Alexander is a knave if and only if Harper is a knave. Assume Alexander is a knight. No contradiction is found in their claim that Harper is a knight and Michael is a knave. Harper cannot be a knight, because this would contradict the false claim of Emily that Alexander is a knave if and only if Harper is a knave. Harper cannot be a knave, because this would contradict the false claim of their own that Emily is a knave or Elizabeth is a knight. We have exhausted all possibilities for Harper, so let us go back and reconsider Alexander. Assume Alexander is a knave. No contradiction is found in their false claim that Harper is a knight and Michael is a knave. Assume Harper is a knight. No contradiction is found in their claim that Emily is a knave or Elizabeth is a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that Michael is a knight or Aria is a knave. Assume Michael is a knight. No contradiction is found in their claim that If Emily is a knave then Aria is a knave. Aria cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Michael is a knight. Assume Aria is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Michael is a knight.