#### Answer

The given statement is false.

#### Work Step by Step

$B \cap C$ is the set that contains elements common to sets B and C.
Notice that the only element common to sets B and C is $1$.
Thus,
$B\cap C=\left\{1\right\}$
$(B\cap C \cup D$ contains the combined elements of $(B\cap C)$ and $D$.
Since the element of $D$ is $4$, then
$\color{blue}{(B\cap C \cup D=\left\{1, 4\right\}}$
Therefore, the given statement is false.