Knights and knaves
On an island, knights always tell the truth and knaves always lie. You meet two people, A and B. A says: "We are both knaves."
What are A and B?
Show hint
Suppose A is a knight. Can a knight truthfully say that?
Show solution
A is a knave and B is a knight.
If A were a knight, the statement would be true, making A a knave, which is a contradiction. So A is a knave, and the statement is false. "Both are knaves" being false while A is a knave means B must be a knight. This "assume, then look for a contradiction" method is proof by contradiction.
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