Inconsistent Sets of Statements from Knights and Knaves
On an island of knights and knaves, knights always tell the truth, knaves always lie, and everyone is either a knight or a knave. There are inhabitants denoted by A, B, C, …. Each one makes a statement about the number of knights in a set. (The set is the empty set with zero knights.) Their vocabulary is rather limited; generally they talk about even and odd numbers.