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In Formal Logic proofs, the contradiction is represented with an inverted T (or upside-down T) as follows: ┴

The contradiction symbol can be introduced at any time a logical contradiction is encounterd, for example, all of the the following contradictory logical statements (using different symbols) can be replaced with the contradiction symbol:

The ball is completely blue and the ball not completely blue.

P ^ ¬P

P & ~P

P & !P

P AND NOT P

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