Regarding sets $A$, $B$, and $C$
$$\begin{aligned}
& \{ ( 1,2 ) , ( 2,3 ) , ( 3,4 ) \} \subseteq A \times B \\
& \{ ( 1,2 ) , ( 3,4 ) , ( 4,2 ) , ( 4,4 ) \} \subseteq A \times C
\end{aligned}$$
it is known that.
Accordingly,\\
I. The set $A \cap B$ has at least 3 elements.\\
II. The set $A \cap C$ has at least 3 elements.\\
III. The set $B \cap C$ has at least 3 elements.\\
which of these statements are always true?\\
A) Only I\\
B) Only II\\
C) Only III\\
D) I and II\\
E) I and III