There is a land where every inhabitant is either of Type X or Type Y. One type always tells the truth, and one type always lies. You meet two inhabitants, A and B.
A:B is of Type X.
B:At least one of us is of Type Y.
Which type tells the truth, which type lies, and what are A and B?
There are 8 possibilities to run through.
The only one that works is:
A is an X, B is a Y, X's are liars, Y's are truth-tellers