De Morgan's Laws (Set Theory)/Set Complement/Complement of Intersection/Proof 1
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Theorem
- $\overline {T_1 \cap T_2} = \overline T_1 \cup \overline T_2$
Proof
\(\ds \overline {T_1 \cap T_2}\) | \(=\) | \(\ds \mathbb U \setminus \paren {T_1 \cap T_2}\) | Definition of Set Complement | |||||||||||
\(\ds \) | \(=\) | \(\ds \paren {\mathbb U \setminus T_1} \cup \paren {\mathbb U \setminus T_2}\) | De Morgan's Laws: Difference with Intersection | |||||||||||
\(\ds \) | \(=\) | \(\ds \overline {T_1} \cup \overline {T_2}\) | Definition of Set Complement |
$\blacksquare$
Sources
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- 2008: Paul Halmos and Steven Givant: Introduction to Boolean Algebras ... (previous) ... (next): $\S 2$