Quiz 2
Discrete Mathematics · 1 problem · solutions hidden, click to reveal
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Problems
On Smullyan's island of knights (who always tell the truth) and knaves (who always lie), you meet A and B. A says "The two of us are both knights" and B says "A is a knave." Determine what A and B are (or draw as much conclusion as possible).
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Answer: A is a knave; B is a knight.
Suppose A is a knight. Then A's statement is true, so A and B are both knights. But B (now a knight) says "A is a knave," which would be false - contradiction. So A is not a knight; A is a knave.
Since A is a knave, B's statement "A is a knave" is true, so B is a knight. (And A's own claim is then false, consistent with A being a knave.)
Conclusion: A is a knave and B is a knight.
Since A is a knave, B's statement "A is a knave" is true, so B is a knight. (And A's own claim is then false, consistent with A being a knave.)
Conclusion: A is a knave and B is a knight.