Let set A be written as B∪C, where B and C are 2 disjoint nonempty subsets of A.
the number of elements of B and C respectively can be:
i) 1, 3
ii)2, 2
for case i we have the following pairs of sets:
{0}, {4,5,7}
{4}, {0,5,7}
{5}, {0,4,5}
{7}, {0,4,5}
for case ii, consider only one of the sets, which can be any of these:
{0,4}, {0,5}, {0,7}, {4,5}, {4,7},{5,7}
Clearly these pairs complement each other, that is if the first set is {0,4}, the second set is {5,7}, if the first set is {0,5} the second set is {4,7}, and if the first set is {0,7} the second is {4,5}.
Thus there are 4+3=7 pairs of subsets
Answer: 7
