I came to a question like the title, which I reckon should be able to express in propositional logic. I am still confused what kind of statements are able to express in propostional logic or predicate logic.
Every nonempty subset of positive integers has a least element.
Here is my interpretation:
Let $X$ be non empty subset.$N(X)$be nonempty subset of natural numbers.$\:L(X)$means exists least element in X.
$$\forall X(N(X)\wedge L(X))\:\text{Here not very sure $\wedge$ or $\implies$}$$
The Negation will be
$$\exists (\neg N(X)\lor\neg L(X)) $$
I am not sure if it's correct, any comments will be appreciated.