Does there exist a bijection between empty sets? 
Does there exist a bijection between empty sets?

What I think is:
Since 'for every $x\in \emptyset$, there exists $y\in \emptyset$ such that $(x,y)\in f$' is false and the negation of this statement is also false because of 'existence' sentence..  
But I think empty sets are equipotent intuitively.
Am I wrong? Help

If a statement starts with '$\forall x \in \emptyset$,...', it is vacuously true. 
Because the set contains no elements, any statement holds for 'all elements' in it.
I'm not sure if this answer is 'mathematical' enough, but I think that's the point you might have missed.
