Sets and Subsets

In fact, is not possible to make any subset B whit more than 11 elements whit this property.

Let's suppose that is possible to make a set with 12 or more elements using this property.

Be B a subset of A with $k\ge 12$ elements. Be $n$ the greater element of B.

$n$ need to have $k$ positive divisors ( $n$ itself and the other $k-1$ elements.

The grater number with $k$ positive integers is $m^{(k-1)}$ . If $m$ is $2$ , we a problem:

$2^{(k-1)}>2^{11}=2048^{2015}$ because $k=12$ . Thus $n>2015\notin B$ what is a contradiction. If $m$ is greater than 2, the same problem appears. It proves that the number of elements in set B can't be 12 or more.

The the answer is 11.