$A=\emptyset $ if and only if $B = A \bigtriangleup B$ Is this true?
If $A$ and $B$ are sets, then $A=\emptyset $ if and only if $B = A \bigtriangleup B$.
If $A=\emptyset$ then $B=\emptyset$ too?
Could someone help me please?

I hope you know that $A\bigtriangleup B=(A\setminus B)\cup(B\setminus A)$.
Then, if $A=\emptyset$, obviously $A\bigtriangleup B=(\emptyset\setminus B)\cup(B\setminus\emptyset)=B$.
For the other direction, note that $A\setminus B$ never is a subset of $B$, unless it is empty. So $A\subseteq B$. But $B\setminus A=B$, so if $A\neq\emptyset$, then $B\setminus A\subsetneq B$. Thus $A=\emptyset$.
