$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?

$A\triangle B$ is the set of elements in either $A$ or $B$ but not both. 
If $A=\emptyset$ then $A\triangle B$ contains all the elements of $B$ and none that are not.
If $B=A\triangle B$ then every element of $B$ is in $A\triangle B$ and no element not in $B$ is in $A\triangle B$, which is only permissible if $A$ is empty. 
So $A=\emptyset \iff A\triangle B=B$

However, a fact of $B=A\triangle B$ places no restraint on the contents of $B$, and $B$ being not empty is no prohibition against $A\triangle B=B$.
