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Proof that P && !P (apenantology) is always false
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| //I propose an apenantology can be represented as P && !P such that this expression is always false | |
| //Proof | |
| P || !P // Tautology, always true | |
| => !(P || !P) // Inverse of tautological statement, always false | |
| => !P && P // Distributive property of && | |
| => P && !P // Commutitive property of && | |
| => P && !P <=> false | |
| QED |
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