Let X be a finite set. A family F of subsets of X is said to be upward closed if the following holds for all sets A,B ⊆ X:
A ∈ F and A ⊆ B ⇒ B ∈ F.
For families F and G of subsets of X, let
F ⊔ G = {A ∪ B : A ∈ F and B ∈ G}.
Suppose F and G are upward closed families. Then which of the following is true?

Correct Answer: A

Let X be a finite set. A family F of subsets of X is said to be upward closed if the following holds for all sets A,B ⊆ X:
A ∈ F and A ⊆ B ⇒ B ∈ F.
For families F and G of subsets of X, let
F ⊔ G = {A ∪ B : A ∈ F and B ∈ G}.
Suppose F and G are upward closed families. Then which of the following is true?

Correct Answer: A