Suppose that f F(X) is monotone and g F() is increasing. Then f supermodular and

Suppose that f ∈ F(X) is monotone and g ∈ F(ℜ) is increasing. Then
f supermodular and g convex ⇒ g ο f supermodular
f submodular and g concave ⇒ g ο f submodular