# Relative Complement with Self is Empty Set

## Theorem

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

$\relcomp S S = \O$

## Proof

 $\displaystyle \relcomp S S$ $=$ $\displaystyle S \setminus S$ Definition of Relative Complement $\displaystyle$ $=$ $\displaystyle \O$ Set Difference with Self is Empty Set

$\blacksquare$