If $A$ and $B$ are subsets of $U=\{1,2,3,4,5\}$ such that $A \cup B = U, A\cap B =\emptyset,$
how many possible choices are there for the ordered pair $(A,B)$?

Details and assumptions

It is possible that $A = \emptyset$ or $B = \emptyset$.

Your answer seems reasonable.
Find out if you're right!