Answer
$\overline{B\cup C} =\{0,5,9\}$
Work Step by Step
$B\cup C$ is the set of elements that are either in B or in C, or in both.
Hence, $B\cup C =\{1,2,3,4,6,7,8\}$.
$\overline{B\cup C}$ is the set of elements of $U$, that are not in $B\cup C.$
Thus,
$\overline{B\cup C} =\{0,5,9\}$