Confused by partial negation

Question

Live bacteria are not present in all yogurt brands.

Does it mean "live bacteria are present in some yogurt brands, but not all" or "there is no bacterium in any yogurt brand"? Or does it depend on the context?

I know that "All yogurt brands do not contain live bacteria." seems to mean "not all yogurt brands contain live bacteria". But what if "all" does not appear at the beginning of a sentence but appear after some preposition such as "in"?

I often confuse this. How should we distinguish between "partial negation" and "complete negation" effectively? I have searched for this, but the answers are quite different.

Answer 1

Live bacteria are not present in all yogurt brands.

This sentence states that there are yogurt brands that contain no live bacteria and, worded as "not ... all", it implies that there are other yogurt brands that do contain live bacteria.

For full negation, you say "not... any", for example,

Live bacteria are not present in any yogurt brands.

Answer 2

I slightly disagree with the other answer. The sentence is slightly ambiguous as written, which is probably why you are having trouble with it. I am sure that what the author MEANT is that some yogurt brands contain live bacteria and some brands don't. But that is based on a priori knowledge of yogurt, not the structure of the sentence. It should have been edited to say "some yogurt brands contain live bacteria and some don't." Or "Live bacteria are present in some but not all yogurt brands."

Without a priori knowledge, the best way to interpret the above sentence is "there exists at least one yogurt brand which does not contain live yogurt." That is not how I would write it, but that is what it actually means.

For example if the sentence said "Violins are not present in all schools" I would be wondering what that meant. But my best guess would be that some or all schools do not contain violins.