# What is this relation between sets : A is not included in B NOR B is included in A? Does it have a name?

The relation " A is not included in B" OR " B is not includde in A" is the relation of distinction ( non-identity).

Does the relation : " reciprocal non inclusion" have a name?

It cannot be disjunction. For, surely two disjoint sets satisfy this relation, but this is not a necessary condition two sets to be disjoint to satisfy the relation in question.

In general, this term applies for any partial order $$\prec$$ when you have $$x$$ and $$y$$ such that neither $$x\prec y$$ nor $$y\prec x$$ are true.