1.11 If 0 is an algebra, m(0) is the minimal monotone class over 0, and ????2 is...

1.11 If ℱ0 is an algebra, m(ℱ0) is the minimal monotone class over ℱ0, and ????2 is defined as

????2 = {B : A ∪ B ∈ m(ℱ0), ∀A ∈ m(ℱ0)}

Then show that ????2 is a monotone class.

Hint: Look at the proof of theorem 1.38 on page 39, and repeat the arguments therein.