$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?

$A \Delta B$  is the set of things that belong to exactly one of $A$ and $B$. 
So, if $A = \emptyset$, then $A\Delta B = (A\backslash B) \cup (B\backslash A) = B$.
If $A\Delta B = B$, then $A\backslash B = \emptyset$, or $A\subset B$, but $B\backslash A = B$ then $A = \emptyset$.
