Are the events d2 and d4 independent do the appropriate

Question

1. Let N = 1000 and let S = {1, 2, ... , N}. Let D_i = {m belongs to S: i|m} for integers i between 1 and N.

a) Are the events D_2 and D_4 independent? Do the appropriate calculation to answer this question. Then explain why your answer makes sense.

b) Are the events D_4 and D_5 independent?

c) Are the events D_5 and D_6 independent?