Let F and G be two σ-algebras of subsets of Ω. Is $F\cup G$, the collection of subsets of Ω lying in either F or G a σ-algebra?
I am able to prove this using an example:-
So their union would be the bigger set G,which is a $\sigma$ algebra already.
based on this can I argue that whenever I am union-ing two $\sigma$ algebras , one will be the subset of the other and so the result would be the bigger set which is already a $\sigma$ algebra?