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A sentence nobody on the island can say

knights-and-knaveslogicself-reference

On the island of knights (always truthful) and knaves (always lying), you overhear someone say:

"I am a knave, or two plus two equals five."

The "or" is the ordinary inclusive one: the sentence is true if at least one of the two parts is true.

Could a knight have said this? Could a knave? What can you conclude about the speaker?

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Two plus two is not five, so the sentence is true exactly when "I am a knave" is true. Now test each type.

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One Question, Two Guards, One DoorCheryl's Birthday and Iterated KnowledgeLogic and QuantifiersProof Techniques: Direct, Contrapositive, ContradictionSelf-Referential Quiz Puzzles

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