Question 159
Consider all pairs $(x, y)$ of real numbers such that $0 \leq x \leq y \leq 1$. Let $M(x, y)$ be the maximum value of the set
$$
A=\{x y, x y-x-y+1, x+y-2 x y\}.
$$
Find the minimum value that $M(x, y)$ can take over all these pairs $(x, y)$.
$$
A=\{x y, x y-x-y+1, x+y-2 x y\}.
$$
Find the minimum value that $M(x, y)$ can take over all these pairs $(x, y)$.