A proper subset of a set A is a subset that is strictly contained in A and excludes at least one member of A. The empty set is also a proper subset of any nonempty set.
So there is only 1 element that a set must have if the number of proper subsets is 1/2 of the total number of subsets.
For example: A = { 4 }
Proper subset : { } ( 1 )
All subsets: { } , { 4 } ( 2 )
1 = 1/2 * 2
Answer: 1 element.