"Or", two or more sentences, at least one of which can be established.

"He", both, or multiple sentences, are true, so it is possible.

A has the largest element, or B has the smallest element.

A contains the largest element, which is true.

Or b contains the smallest element, which is true.

Or at least one of these two sentences is true.

There is no largest element in A, and there is no smallest element in B.

Does not contain the largest element. This sentence holds.

And b does not contain the smallest element. This sentence holds.

And it shows that these two sentences are valid at the same time.

If you are satisfied, please accept my answer. Thank you.

If you have any questions, please ask.