The exercise is taken from Rudin, principles of mathematical analysis, chapter 2 ex. 1.
Let $A$ a set and let also $B$ such that $A \cap B = \emptyset$ This implies:
$$ \emptyset = A \cap B \subseteq A, $$
For given $A$ the set $B$ can always be found, for example take $B = A^C$, the complement of $A$. Is such proof correct?