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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.

Show that the statements are inconsistent!

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Inconsistent Sets of Statements from Knights and Knaves