Although as students we learn addition before we learn about sets, from the viewpoint of mathematics, sets are everywhere / everything can be expressed in terms of sets, so there's no point talking about sets in any given problem (unless it involves matters deep in set theory, which this does not). This is evident even colloquially, where we can talk about problems without explicitly using the word “set” — for example, “given some numbers, how many can you pick such that no two of them add up to another?” — while it's hard to avoid using “add” or “addition”.

So this problem is really more about addition than about sets, as the mathematicians who worked on it will say: the amount of set theory it involves is very little/almost nonexistent, while the properties of addition it involves are fairly deep.

(But sure, no harm if sets were mentioned in the title, I guess!)