The preference relation satisfies monotonicity if for all x, y X, if xk yk for all k, then x y, and if xk > yk for all k, then x y.

The preference relation satisfies strong monotonicity if for all x, y X, if xk yk for all k and x y then x y.

Show that preferences represented by min{x1, x2} satisfy monotonicity but not strong monotonicity