Regarding sets $A$, $B$ and $C$
$$\begin{aligned}
& s(A) = s(C) = 5 \\
& s(A \times (B \cup C)) = 30 \\
& s(B \times (A \cup C)) = 16
\end{aligned}$$
Given these equalities.
Accordingly, how many elements does the set $B \cap C$ have?
A) 1
B) 2
C) 3
D) 4
E) 5