how is it possible that the smallest set is black cards and clubs vs queens and spades?

I must have misunderstood the question as well. Two of the choices cannot intersect, leaving black cards and clubs & queens and spades. I took the question to mean which of the remaining two had the smaller intersection. However, upon reading your question / their answer, I would agree that it is asking which intersection IS ONE OF THE SETS (which means set B is inside set A) not which intersection is smaller. Took me a bit but now I understand why the answer is Black/Clubs.

Hey Giordano, Thank you for reaching out! The question asks which of the 4 intersections represents the smaller of the 2 sets. Let's look at the intersection between the set of all Black cards (26 elements) and all Clubs (13 elements). Since all Clubs are black, the Clubs set is in fact a subset of the Black cards set. Therefore, the intersection between the two sets is indeed the Clubs set (the smaller of the two). On the contrary the intersection between the set of all Queens (4 elements) and the set of all Spades (13 elements) is a set consisting of only one element - the Queen of Spades. Therefore, this cannot be the correct answer. Hope this helps! Kind regards, 365 Hristina