I need to prove this $|A-B|=|B-A|\rightarrow|A|=|B|$ I managed to come up with this:
let $f:A-B\to B-A$ while $f$ is bijective.
then define $g\colon A\to B$ as follows: $g(x)=\begin{cases} f(x)& x\in (A-B) \\ x& \text{otherwise} \\ \end{cases}$
but I'm not managing to prove this function is surjective.
Is it not? or am I on the right path? if so how do I prove it?
Thanks