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.
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.