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