1.6 A -Algebra does not necessarily contain all the events in Let = {A | A countable or Ac is countable}. Show

1.6 A σ-Algebra does not necessarily contain all the events in Ω

Let ℱ = {A ⊆ Ω| A countable or Ac is countable}. Show that ℱ is a σ-algebra.

Note that, if Ω is uncountable, it implies that it contains a set A such that both A and Ac are uncountable and thus A /∈ ℱ .