try proving this "in-between" step:

for the first problem-

show that if k < m, that (D_{k})U(D_{m}) = (-m,1/k). what is the smallest k can be, and what is the largest m can be?

for the second problem-

show that for k < m that (D_{k})∩(D_{m}) = (-k,1/m). again: how small can k be, and how large can m be?

(the answer for k in both cases should be "easy". answering for m might take a little thought).

try drawing a picture with k = 3, and m = 4. draw another one with k = 1, and m = 10. what do you notice?