Answer
$\overline{B \cup C}=\left\{0, 5, 9\right\}$
Work Step by Step
RECALL:
(1) $\overline{C}$ is the complement of set $C$, which is the set that contains the elements of the universal set that are not elements of $C$.
(2) $\cup$ represents the union of two sets, which is the set that contains the combined elements of the two given sets.
Use (2) above to obtain:
$B \cup C=\left\{1, 2, 3, 4, 6, 7, 8\right\}$
Use rule (1) above to obtain:
$\overline{B \cup C}=\left\{0, 5, 9\right\}$
