(a) Let n >= 2. We select n + 1 different integers from the set {1, 2, ..., 2n}. Is it true that there will always be two among the selected integers so that one of them is equal to twice the other?

(b) Is it true that there will always be two among the selected integers so that one is a multiple of the other?

My attempt:

(a) is false. A counterexample for n = 5: {1, 3, 4, 5, 7, 9}.

I think (b) is true but cannot seem to prove it. Any ideas?