De Morgan's Laws (Set Theory)/Set Complement/Complement of Intersection/Corollary

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Theorem

Let $T_1, T_2$ be subsets of a universe $\mathbb U$.


Then:

$T_1 \cap T_2 = \overline {\overline T_1 \cup \overline T_2}$


Proof

\(\ds T_1 \cap T_2\) \(=\) \(\ds \overline {\overline {T_1 \cap T_2} }\) Complement of Complement
\(\ds \) \(=\) \(\ds \overline {\overline T_1 \cup \overline T_2}\) De Morgan's Laws: Complement of Intersection

$\blacksquare$


Sources