Relative Complement with Self is Empty Set

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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

$\blacksquare$


Also see


Sources