Both Knights Or Knaves
Edgar Abercombie was an anthropologist who was particularly interested in the logic and sociology of lying and truth-telling. One day, he visited the island of Knights (who always tell the truth) and Knaves (who always lie), and met two people, Andrew and Benard.
Andrew says: We are both the same type - that is, we are either both knights or both knaves.
What fact can we deduce?
This problem is taken from Raymond M. Smullyan's book Logical Labyrinths.
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It helps to write out the possible cases. Either Andrew is a knight or a knave. Under each of these cases, write out the sub-possibilities. If Andrew is a knight, the only possible breakdown is that 'Andrew is a Knight and Bernard is a Knight' (sine, if he is a knight then he is telling the truth about being of the same type). If Andrew is a knave (so it's not the case that they are of the same type, or in other words, Andrew is one type and Bernard the opposite type), the only possible breakdown is that 'Andrew is a Knave and Bernard is a Knight'. In both cases Bernard comes out as a Knight.