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 $\quad$

$\blacksquare$