If $(\cdot)$ is the bitwise XOR operation and $X$ and $Y$ are any two binary numbers, then $Z$ is the bitmask such that:
\begin{align}X(\cdot)Y&=Z \\ X(\cdot)Z&=Y\\ Y(\cdot)Z&=X \end{align}
Now how do I prove that:
For some $W$ (a binary number) such that $W\neq Z$ , $$X(\cdot)W=Y$$ does not exist?