#### Answer

$(B\cap C)'=\left\{a, b, c, d, f, g\right\}$

#### Work Step by Step

$\cap$ represents intersection of sets.
The intersection of two sets is a set that contains the elements that are common to both sets,
Thus,
$B\cap C = \left\{e\right\}$
RECALL:
The complement of set A, represented by $A'$, is the set that contains all the elements of the universal set $U$ that are not elements of $A$.
Thus, the complement of $B\cap C$ is:
$(B\cap C)'=\left\{a, b, c, d, f, g\right\}$