Complement of Empty Set is Universe

Theorem
The complement of the empty set is the universe:


 * $$\complement \left({\varnothing}\right) = \mathbb U$$

Proof
Substitute $$\mathbb U$$ for $$S$$ in $$\complement_S \left({\varnothing}\right) = S$$ from Relative Complement of Null.

Also see

 * Complement of Universe