Quoted By:
It's not hard.
1) prove that the supremum of A cant be higher than the infinite of B using the first premise, because that would imply that there is an intersection, which would in turn imply that there is an element of A that's equal to instead of lower than an element of B
2) prove that the supremum of A cant be lower than the infimum of B, because their arithmetic mean would be in neither set, and that would contradict premise 2
3) deduce that the infimum of B and the supremum of A have to be equal to a c, which has to be contained in only one of the sets
