Please consider the following. Either prove or give a counter-example.
If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$
Please consider the following. Either prove or give a counter-example.
If $\large 0\le a\le x\le 1~\&~0\le b\le y\le 1$ then $\large a+b-a\cdot b\le x+y-x\cdot y$
This is related to "probability of union" post, yes?
It appears true, I haven't been able to find a counter example but also haven't been able to prove it (yet).