The lower bound of liking both A and B is 50%, while the upper bound is 70%. In terms of Venn diagrams, I think of it like this: try to "push apart" the regions A and B. A can be pushed out of B, but only to a point, since B covers 80% of the space. In fact we can push 20% of A out of B. The other 50% of A remains in B, so then the lower probability 50%, this part of A remaining in B. For the upper probability, try to "push together" A and B. A can fit completely in B, and the upper probability is the area of A, 70%.
Another way to think of lower probability is as the "worst case scenario" for how much A and B overlap. At worst, A and B can be only partially apart, and the amount they must overlap is the lower probability, 50% of the total area. The upper probability then is the "best case scenario" that A sits completely in B.
Of course these intuitions can be made precise, but this is a way I found it helpful to think about it!