# Union of Intersections of 2 from 3 equals Intersection of Unions of 2 from 3

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## Theorem

Let $A$, $B$ and $C$ be sets.

Then:

- $\paren {A \cap B} \cup \paren {B \cap C} \cup \paren {C \cap A} = \paren {A \cup B} \cap \paren {B \cup C} \cap \paren {C \cup A}$

## Proof

## Sources

- 1975: T.S. Blyth:
*Set Theory and Abstract Algebra*... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems: Exercise $13$