Answer
$\{0,5,9\}$
Work Step by Step
$\overline{B}$ = set of elements that are in the universal set, but not in B
0 is not in B, so it is in $\overline{B}$,
1 is not in B, so it is in $\overline{B}$,
2 is in B so it is not in $\overline{B}$,
3 is not in B, so it is in $\overline{B}$,
and so on, testing each element of U
Hence,
$\overline{B}$ = $\{0,1,3,5,9\},\quad$
$\overline{C}$ = set of elements that are in the universal set, but not in C
$\overline{C}$ = $\{0,2,5,7,8,9\}$
$\overline{B}\cap\overline{C}$ is the set of elements that are in both $\overline{B}$ and $\overline{C}$ .
Thus,
$\overline{B}\cap\overline{C}$ = $\{0,5,9\}$
