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 with Self is Empty Set.

Also see

 * Complement of Empty Set is Universe