Is the intersection and subset of items a subset? (set theory)

Let's say I have set A, B, C and D (this can vary). I want to perform an intersection of A, B and C and the result of that I want to get a subset based on D (d is a fixed quantity, for example, d wants exactly 3 items, which would be a subset of the result of the intersections of the other sets).

What's the name of this? What should I call the class that performs these operations? I was thinking SubsetOfSets, but sometimes the class should only perform an intersection without getting a fixed number of items (subsets).

I'm reading about sets theory and the naming it's a little confusing.

Have you tried stack overflow? They may have some qs and answers to something like this. Sorry if that isn't what you're looking for/isn't related.

wpsokw said:

Have you tried stack overflow? They may have some qs and answers to something like this. Sorry if that isn't what you're looking for/isn't related.

Click to expand...

Nope. I'm not a junior programmer at all, and still they few answers I post get always downvoted. I found the community very petty and unwelcoming. I'm sure if I post this question it'll be downvoted and closed for being too broad, off-topic or not clear enough or some stupid shit like that.

Just did a quick serach on naming and it's exactly what I expected:

Ended up asking in the stackexchange network and the result was not bad at all. I got some really good answers. I'm actually glad I asked.

(I also asked another question on both wordpress.stackexchange and stackoverflow and they closed the question on both sites, even though someone actually answered the question in the comments (LMAO) (just shows how flawed their system is, anyway....))