Showing if a function is injective or surjective problem $F : \Bbb{P}(X) \rightarrow \Bbb{P}(X) ; U \rightarrow (U-A) \cup (A-U)$
My intuition has been telling me that this function is bijective but I having the most difficult time trying to show this. Any help would be appreciated, thank you!!
edit: So far, I introduced sets $U_1$ and $U_2$, I am assuming $f(U_1)=f(U_2)$ and trying show $U_1=U_2$ in order to show injection. So I have $(U_1-A)\cup(A-U_1)=(U_2-A)\cup(U_2-A)$ and I'm unfamiliar with how to manipulate this into $U_1=U_2$. I haven't worked much with set notation before.
As for showing that f is surjective, I've tried drawing some Venn diagrams to help me process the question but I'm not sure where to go. Thank you for the quick replies!

Hint $\Delta$ is associative, hence
$$A \Delta  (A \Delta W)= (A \Delta A) \Delta W=W$$
