If $A \triangle B=A$, then $ B= \emptyset$.
This seems simple enough, as an idea. I mean if the set $B$ is anything but empty, $A\triangle B$ would contain more or less than simply $A$, simple examples would be two disjoint sets or two intersecting sets or whenever $A=B$. But how do I prove it formally?
The example I gave feels like I can make it work with a contrapositive: If $B$ is not empty, $A\triangle B$ does not have the same elements as $A$.