Let $A , B$ be non-empty subsets of $\mathbb { R } ^ { 2 }$. Pick the correct statement(s) from below:\\
(A) If $A$ is compact, $B$ is open and $A \cup B$ is compact, then $A \cap B \neq \varnothing$.\\
(B) If $A$ and $B$ are path-connected and $A \cap B \neq \varnothing$ then $A \cup B$ is path-connected.\\
(C) If $A$ and $B$ are connected and open and $A \cap B \neq \varnothing$, then $A \cap B$ is connected.\\
(D) If $A$ is countable with $| A | \geq 2$, then $A$ is not connected.