In context of the inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, A and B. Determine what A and B are if they address you as: A says "The two of us are both knights" and B says "A is a knave."

Question

Mathematics

Daniela Dean

11 January, 00:34

In context of the inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two people, A and B. Determine what A and B are if they address you as: A says "The two of us are both knights" and B says "A is a knave."

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Answers (1)

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Skylar Tucker · Answer 1

A is a knave

B is a knight

Step-by-step explanation:

If A is telling the truth, then both are knights and B cannot be lying. However, since B claims that A is a knave, they can't be both knights, and there is no possible way that A is a knight.

If A is knave and thus is lying, they aren't both knights. Since B claims A is a knave, his statement can be true and thus B can be knight and A will be knave.