## 142. The First Island

On the first island, our philosopher met two native inhabitants A and B, who stated:

A: B is a knight, and this island is called Maya.

B: A is a liar, and this island is called Maya.

Can we assert that the first island is indeed called Maya?
142. Suppose V is a knight. Then the first island is called Maya, and moreover, A is a liar. Therefore, the statement made by A is false, and thus it is not true that V is a knight and the first island is called Maya. But by the assumption, V is a knight, so the first part of the statement is true. Hence, we conclude that the second part of the statement is false. Therefore, the first island is not Maya. Thus, if V is a knight, the first island must both be and not be Maya. The contradiction obtained proves that V is a liar.

Since V is a liar, A is also a liar (since A claims that V is a knight). The statement made by V, like any statement made by a liar, is false, so it is not true that A is a liar and the first island is called Maya. But the first part of the statement is true (since A is a liar). Therefore, the second part of the statement must be false, and the first island is not Maya.