Inclusion–exclusion for two sets

Builds on Cardinality of a finite set Rule of sum

Statement

Let $A$ and $B$ be finite sets. Then $|A \cup B| + |A \cap B| = |A| + |B|.$ Equivalently, $|A \cup B| = |A| + |B| - |A \cap B|$ .

Remarks

If $A \cap B = \varnothing$ , this is the rule of sum. For three sets: $|A \cup B \cup C| = |A| + |B| + |C| - |A \cap B| - |A \cap C| - |B \cap C| + |A \cap B \cap C|$ . The inclusion–exclusion principle is the version for $n$ sets.

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Cardinality of a finite set definition
Rule of sum statement
Inclusion–exclusion for two sets statement

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2 pages build on this one.

Tag	`0C4YEQ9H5E`
URI	`m2://0C4YEQ9H5E`
Kind	statement, theorem
Writing	W0 stub
MSC	05A05
Status	This copy of the site has no build data. Run `m2 status 0C4YEQ9H5E`.
Uses	Cardinality of a finite set, Rule of sum

Inclusion–exclusion for two sets

Statement

Remarks

Reading path

Where this leads

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