John:Has B ever said that you are a liar?
A answered, either "Yes" or "No."
John:Is B a liar?
A answered, either "Yes" or "No."
The next day, another logician named Jack went to the Land of Knights and Liars. He met the same two inhabitants, A and B. He also asked A two questions.
Jack:Has B ever said that you are both liars?
A answered, either "Yes" or "No."
Jack:Is B a liar?
A answered, either "Yes" or "No."
One of the two logicians, John and Jack, could figure out what types A and B were, but the other logician could not figure out their types. What are A and B?
