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
- 1968: A.A. Sveshnikov: Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions (translated by Richard A. Silverman) ... (previous) ... (next): $\text I$: Random Events: $1$. Relations among Random Events: Example $1.3$