it's ok that every subset has at least 2004 elements, and at most 2006 elemnts. If we have subset with 2006 elemts, then the maximal number of subsets is 2. If we don't have subset with 2006 elemnts: 1) If we don't have subset with 2004 elemnts maximal number is 2006. Subsets with 2005 elements. 2) we have subset with 2004 which doesn;t contain numbers $a$ and $b$. Now we can at most 2004 subsets with 2005 because it can't contain $a$ and $b$. Hence 2006 is max