I have a problem which s related to this symmetric propety.

Show that there exist a unique set $\displaystyle N$ such that $\displaystyle (A \Delta N)=A$ for all $\displaystyle A$. The set $\displaystyle N$ is obviously the empty set. But then how do I prove the uniqueness part of $\displaystyle N$, i.e. if $\displaystyle (A \Delta N1)=A$ and $\displaystyle (A \Delta N2)=A$, then $\displaystyle N1=N2$= the empty set