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So according to wikipedia a set of connectives is complete if and only if it doesnt belong to one of the listed groups. One of the groups is , connectives that are falsehood preserving, that is,that assigning a value of false to all the variables can never produce an output of true.

So clearly XOR has this property, and so $\{XOR\}$ I could conclude heuristically is not complete.

But this still doesnt really show me why. Essentially it is just using previous results proved.

But I am wanting to know, is there any way I can show that one of the four 1-ary Boolean functions cannot be represented by a falsehood preserving connective? Because if I could do that, then I could make sense of it. Thanks

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1 Answers1

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$\neg$

(This would be the shortest answer ever if so short answers were allowed)

Hagen von Eitzen
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