https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Licli&feedformat=atomAoPS Wiki - User contributions [en]2024-03-29T10:06:01ZUser contributionsMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=Principle_of_Inclusion-Exclusion&diff=86174Principle of Inclusion-Exclusion2017-06-26T02:53:02Z<p>Licli: /* Examples */</p>
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<div>The '''Principle of Inclusion-Exclusion''' (abbreviated PIE) provides an organized method/formula to find the number of [[element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets.<br />
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== Remarks ==<br />
Sometimes it is also useful to know that, if you take into account only the first <math>m\le n</math> sums on the right, then you will get an overestimate if <math>m</math> is [[odd integer | odd]] and an underestimate if <math>m</math> is [[even integer | even]].<br />
So, <br />
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and so on.<br />
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== Examples ==<br />
2002 AIME I Problems/Problem 1<br />
http://artofproblemsolving.com/wiki/index.php?title=2002_AIME_I_Problems/Problem_1#Problem<br />
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== See also ==<br />
* [[Combinatorics]]<br />
* [[Overcounting]]<br />
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[[Category:Combinatorics]]</div>Licli