How to prove that given quotation is not a distribution function

Question

I have function

$F(x,y)=\begin{cases} 1, \text{ if } x+y \geq 0, \\ 0, \text{ if } x+y<0 \end{cases}$.

I have no idea how can I prove that given quotation is not a distribution function. Only one think I know is $\Delta_sF \geq 0$.

Answer 1

$F(1,1)-F(1,-1)-F(-1,1)+F(-1,-1)=-1 <0$ so $F$ is not a distribution function. [In terms of random variable this means $P\{-1<X\leq 1,-1<Y\leq 1\} <0$!].