A U ∅ = A Let x ∈ S, where S is the universal set. First we show that if A ∪ Ø ⊂ A. Let x ∈ A ∪ Ø. Then x ∈ A or x ∈ Ø. by definition of the empty set, x cannot be an element in Ø. So by assumption, x ∈ A ∪ Ø, x must be in A. So A ∪ Ø ⊂ A. Next, we show that A ⊂ A ∪ Ø. This is true because the set resulting from the union of two sets contains both of the sets forms the union Since A ∪ Ø ⊂ A and A ⊂ A ∪ Ø, we have that A ∪ Ø = A.
