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Let X be a set and let F1,F2 ⊆ P(X) be two σ-algebras on X. Let...

Let X be a set and let F1,F2 ⊆ P(X) be two σ-algebras on X. Let G := {A ∩ B | A ∈ F1, B ∈ F2}. Prove the following statements:

(1) G is closed under finite intersections.

(2) σ(G) = σ(F1 ∪ F2).

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