Principle of Inclusion-Exclusion: Difference between revisions
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=== Statement === | === Statement === | ||
If <math>(A_i)_{1\leq i\leq n}</math> are finite sets, then: | |||
<math> \left|\bigcup_{i=1}^n A_i\right|=\sum_{i=1}^n\left|A_i\right| | |||
-\sum_{i < j}\left|A_i\cap A_j\right| +\sum_{i<j<k}\left|A_i\cap A_j\cap A_k\right|-\ \cdots\cdots\ +(-1)^n \left|A_1\cap\cdots\cap A_n\right| </math>. | |||
=== Examples === | === Examples === | ||
Revision as of 12:04, 18 June 2006
Statement
If 
are finite sets, then:
.
