Question

How many distinct pairs of disjoint non-empty subsets of A are there, the union of which is all of A?

Answer 1

A = {1, 2, 5, 6, 8}
{1} U {2, 5, 6, 8} 
{2} U {1, 5, 6, 8} 
{5} U {1, 2, 6, 8} 
{6} U {1, 2, 5, 8} 
{8} U {1, 2, 5, 6} 
{1, 2} U {5, 6, 8} 
{1, 5} U {2, 6, 8} 
{1, 6} U {2, 5, 8}
{1, 8} U {2, 5, 6} 
{1, 2, 5} U {6, 8} 
{1, 2, 6} U {5, 8}
{1, 2, 8} U {5, 6}
{1, 5, 6} U {2, 8}
{1, 5, 8} U {2, 6}
{1, 6, 8} U {2, 5} 
The answer is 15 distinct pairs of disjoint non-empty subsets.