Answer
$\bar B\cap \bar C=\{0,5,9\}$.
Work Step by Step
The given sets are
$B=\{2,4,6,7,8\},C=\{1,3,4,6,\}$ and $U=\{0,1,2,3,4,5,6,7,8,9\}$
The symbol $ \bar {B}$ means the set containing the elements of the union set not in set $B$.
$ \bar {B} =\{0,1,3,5,9\}$
The symbol $ \bar {C}$ means the set containing the elements of the union set not in set $C$.
$ \bar {C} =\{0,2,5,7,8,9\}$
The symbol $\cap$ means the set containing common elements of the given sets.
$\bar B\cap \bar C=\{0,5,9\}$
Hence, the answer is $\bar B\cap \bar C=\{0,5,9\}$.
