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Why would truth preservation prevent it from being functionally complete? How can you even tell a truth table is truth preserving? A truth table is not a logical argument.


Truth-preserving in this context means that the function value is true if all function arguments are true. If you only have truth-preserving functions available, then you can not output false if all inputs are true, hence you can not build all possible functions. An analog argument applies to falsehood-preserving functions.


I see. I wasn't familiar with that term in this context, thanks.




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