Answer
$\overline {B\cup C}=\{0,5,9\}$.
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 $\cup$ means the set containing all the elements of the given sets.
$B\cup C=\{1,2,3,4,6,7,8\}$
The symbol $ \overline {B\cup C}$ means the set containing the elements of the union set not in set $B\cup C$.
Hence, the answer is $\overline {B\cup C}=\{0,5,9\}$.
