Prove whether this is true or false: For every two sets $A$ and $B$, $\{A\oplus B, A\cap B\}$ is a partition of $A \cup B$.

Question

I am having trouble with this question. Does anyone have an idea?

Answer 1

If $B = \emptyset$ and $A\ne\emptyset$ then $\{A\oplus B, A\cap B\} = \{A,\emptyset\}$ is NOT a partition of $A\cup B =A$