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Can anyone help to explain the logic behind puzzle 1 thanks!!

Please correct me if I'm wrong but this is what I wrote and I somehow stumbled to the answer.

Without keying in the information that only a Knave can lie and therefore the statement is false, how is the computer able to deduce that Aknight is false or true just base on the initial condition that A can either be a Knight but not both. And how is the computer able to deduce that the statement is false?

Thanks for the help!!

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We know "both are knafes" is false, because otherwise AKnight would be true. AKnight is not allowed to be true at the same time with AKnave (Not(And(AKnave, AKnight)). So AKnave must be true. By this we are able to deduct that BKnave must be false, because otherwise "both are knafes" would be true.

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