Complement of Complement
From ProofWiki
Theorem
The complement of the complement of a set is the set itself:
- $\complement \left({\complement \left({S}\right)}\right) = S$
Proof
Substitute $\mathbb U$ for $S$ and $S$ for $T$ in $\complement_S \left({\complement_S \left({T}\right)}\right) = T$ from Relative Complement of Relative Complement.
$\blacksquare$
Sources
- Allan Clark: Elements of Abstract Algebra (1971)... (previous)... (next): $\S 8 \beta$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 6.6$
