Complement of Complement

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Theorem

The complement of the complement of a set is the set itself:

$\map \complement {\map \complement S} = S$


Proof

Substitute $\mathbb U$ for $S$ and $S$ for $T$ in $\relcomp S {\relcomp S T} = T$ from Relative Complement of Relative Complement.

$\blacksquare$


Sources