This question is about an island of knights and knaves, where knights always speak the truth and knaves always lie. You encounter two people A and B. Determine, if possible, what each of them are if they address you as follows: A says "B is a knave" and B says "A is a knight".
Here's my solution:
Let p be the proposition 'A is a knight' and let q be the proposition 'B is a knight.'
p q F F x A cannot speak the truth F T x B cannot lie T F x B cannot speak the truth T T x A cannot lie
Therefore, all possibilities are eliminated, so this means that the identity of A and B cannot be deduced.