set confusion
Now here is what I think the last part means:
i. Set is a set with some sets in it. T is just a plain old set. T may or may not be a part of S, but they are both made up of the same big U of numbers. The intersection of T with US would give you any elements in any of the sets in S that are in T too. This is the same thing as taking the U of all of the intersections of T with each set in S.
ii. The union of T with the intersection of all the elements in S would be all of the elements in T plus any elements that are in every set in S, but not in T. This is the same thing as creating the union of T with each set in S individually then taking the intersection of the sets formed when you do that.
Am I understanding this correctly?