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In logic, a contradiction refers to a situation where two statements or propositions cannot both be true at the same time because they express mutually exclusive ideas. A contradiction arises when one statement directly negates or opposes another. In formal logic, a contradiction occurs if a proposition $P$ and its negation $\neg P$ are both asserted as true ____ __________ __________ ______ _________ ______ _______ _________ _________ _________ ______.
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