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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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