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are contradictories if it has to be the case that one is true and the other is false. Two propositions are contraries if at most one of them can be true, but leaves open the option that both of them might be false, which is not possible in the case of contradictories. Contradictories follow the law of the excluded middle but contraries do not. For example, the sentence "the exact number of marbles in the urn is either 10 or not 10" presents two contradictory alternatives. The sentence "the exact

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