If you contradict something, you deny the truth of it and instead preach the opposite to the statement as gospel.
If I say "George Washington" and you say "Abe Lincoln", we're not contradicting each other - both answers are correct, as both are truth.
If you say "Contradiction is someone giving a correct answer to a question and someone then giving another correct answer" and I say "Contradiction is denying the truth of a statement", then that is contradiction.
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