Complement of Universe is Empty Set

Theorem
The complement of the universe is the empty set:


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

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

Also see

 * Complement of Null