Here is the problem:
List 5 elements of this set:
${\{(X, Y)\}\in\\} \mathcal {P}\{1,2,3\} \times \mathcal{P}\{1,2,3\}:X\cap Y= \emptyset\ \}$
I know that: $${\mathcal{P }(\{1,2,3\}= {\{\emptyset,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}}}$$
Does this involve taking massive Cartesian products? The intersection between two sets is disjoint when they have no other like elements, but I don't get how to find the intersection between the product of power sets as an empty set or disjoint?