What's the negation of “At least three of the sentence are false”? Following with the question I asked before
What's the negation of "One of the sentence is false"?
The negation of “At least three of the sentence are false” would be "any, one or two of the sentence is/are false"?

With f-o logic, the original statement is:

$\exists x \ \exists y \ \exists z \ [(x \ne y \land x \ne z \land y \ne z) \ \land \ (False(x) \land False(y) \land False(z))]$.

Thus, negeatin it:

$\forall x \ \forall y \ \forall z \ \lnot [(x \ne y \land x \ne z \land y \ne z) \ \land \ (False(x) \land False(y) \land False(z))]$,

i.e.

$\forall x \ \forall y \ \forall z \ [(x \ne y \land x \ne z \land y \ne z) \ \to \ \lnot (False(x) \land False(y) \land False(z))]$,

i.e.


$\forall x \ \forall y \ \forall z \ [(x \ne y \land x \ne z \land y \ne z) \ \to \ ((False(x) \land False(y)) \to \lnot False(z))]$.


The final formula matches with the "informal" negation of the original statement:

"there are at most two false sentences."

