# Relative Complement of Empty Set

## Theorem

The relative complement of the empty set is the set itself:

$\complement_S \left({\varnothing}\right) = S$

## Proof

 $\displaystyle \complement_S \left({\varnothing}\right)$ $=$ $\displaystyle S \setminus \varnothing$ $\quad$ Definition of Relative Complement $\quad$ $\displaystyle$ $=$ $\displaystyle S$ $\quad$ Set Difference with Empty Set is Self $\quad$

$\blacksquare$