83. The Mysterious Accuser.

In another case on the same island, two local residents, X and Y, were tried for a certain crime. The case was highly unusual because it was known that the accuser was either a knight or a liar. At the trial, the accuser made the following two statements:

1) $X$ is guilty.
2) X and Y cannot both be guilty.

What conclusion would you draw from these statements if you were on the jury? Can anything be said about the guilt of $\mathrm{X}$ or Y? Who do you think the accuser is: a knight or a liar?
83. Suppose the prosecutor were a liar. Then statements (1) and (2) would be false. But if statement (1) is false, then X is not guilty, and if statement (2) is false, then both X and Y are guilty. Thus, X would have to be guilty and not guilty at the same time, which is impossible. Therefore, the prosecutor must be a knight. Hence, X is actually guilty, and since X and Y cannot be guilty at the same time, Y must be not guilty. Therefore, X is guilty, Y is not guilty, and the prosecutor is a knight.