(english is not my native language)
Hello everyone, I'm currently stuck at a task.
Let Ω be a set and A, B ⊆ Ω. Let Z = {A, B}. Show that $⟨Z⟩_{Dyn} = ⟨Z⟩_{σ−Alg}$ applies when $( A ∩ B)$,$( A^{c}∩ B)$, $( A∩ B^{c})$ or $( A^{c}∩ B^{c})$ are empty.<
I don't really get this because we got an example of a Dynkin system, which is not an Algebra:
Let Ω be finite with a straight number of elements and D={A ⊆ Ω $ \vert $ A has a straight number of elements}, where D is not an algebra when #$Ω \ge 4 $. <
Now if we, for example, let Ω={A,B,C,D} with 2 subsets X={A,B} and Y={C,D} then the intersection would be empty but according to the inital task that shoudln't be possible or did I miss something?