# MA375: Lecture Notes

Fall 2008, Prof. Walther

## Inclusion-Exclusion Principle (Basic)

Let B and C be subsets of a given set A. To count the number of elements in the union of B and C, we must evaluate the following:

$|B \cup C| = |B| + |C| - |B \cap C|$

Subtracting $|B \cap C|$ corrects the overcount.

In general,

$\displaystyle |A_1 \cup A_2 \cup ... \cup A_n| =$

$\displaystyle |A_1| + |A_2| + ... + |A_n|$

$\displaystyle - |A_1 \cap A_2| - |A_1 \cap A_3| - ... - |A_(n-1)\cap A_n|$

$\displaystyle + |A_1 \cap A_2 \cap A_3| + |A_1 \cap A_2 \cap A_4| + ... + |A_(n-2) \cap A_(n-1) \cap A_n|$

$\displaystyle + (-1)^(n+1)|A_1 \cap A_2 \cap A_3 \cap ... \cap A_n|$

## Alumni Liaison

Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva