# Cardinality of Set Union/3 Sets

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## Theorem

Let $S_1$, $S_2$ and $S_3$ be finite sets.

Then:

 $\ds \card {S_1 \cup S_2 \cup S_3}$ $=$ $\ds \card {S_1} + \card {S_2} + \card {S_3}$ $\ds$  $\, \ds - \,$ $\ds \card {S_1 \cap S_2} - \card {S_1 \cap S_3} - \card {S_2 \cap S_3}$ $\ds$  $\, \ds + \,$ $\ds \card {S_1 \cap S_2 \cap S_3}$

## Proof

This is a specific example of Cardinality of Set Union: General Case.

$\blacksquare$