I was trying to be quick and got this one wrong but after seeing the answer it became so obvious. For anyone else who got it wrong all this fancy language breaks down to is the fundamental idea that in Bi-Conditionals all either must be true or must be false. In this question we see that one instance was not true therefore the vase was not purchased and all you need to do is find the answer choice that has the mismatch IE which one has the out of place claim .

@BraedenB Stared at my computer screen for 10 min but i finally put it together. It doesn't say anywhere that they MUST be cited late if they are beyond 5 minutes, we are only told that to be cited you have to meet the 5+ condition. A way to think of it is like this, you can be late and simply not be cited, maybe you sneak in, have a note, etc. But if you are cited you must be 5+

The way it is laid out in the arrow example of Super set Necessary subset. was initially confusing. But i parsed it like this. You have to be (necessary) in the USA if you are in New York that must be true 100 percent of the time. However being in New York means you are in the USA (sufficient) But you do NOT HAVE to be (necessary) in New York to be in the USA. Maybe this will help someone