Solution: Note that since $A \cap B = \emptyset $ so the intersection of $X \cap A$ and $X \cap B$ will also be empty. Also, as the sets $A$ and $B$ are open and close simultaneously, the sets $X \cap A$ and $X \cap B$ will also be close and open simultaneously (as finite intersection of open (closed) sets is open (closed)). Therefore, $X \cap A$ and $X \cap B$ are separated sets.