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Inclusion-Exclusion Principle

```Date: 09/03/2002 at 19:56:57
From: Rehana Chandarpal
Subject: Sets

In a survey of 100 people, 85 like calypso and 93 like pan. Calculate
the number of people who like both calyso and pan.

I tried answering this question by doing the equation that my teacher
showed me but I still can't do it.
```

```
Date: 10/18/2002 at 17:27:22
From: Doctor Nitrogen
Subject: Re: Sets

Hi, Rehana:

Why don't we let a capital letter like X denote a set? And we'll use
#X to denote the number of elements in set X.

Let U be the set with 100 people in it, let A be the subset of U that
has all the people who like calypso, let B be the subset of people in
U who like pan, and let C be the subset of people in U who like both
calypso and pan. Then

#U = 100.

#A = 85

#B = 93

#C = (unknown).

To find #C, use the fact that the total number of people in U equals
the total number of people in A plus the total number of people in B,
minus the total number of people in C, so

#U = #A + #B - #C
or
100 = 85 + 93 - #C

Can you figure the rest out now? This way of solving a math problem
like this one uses what is called the "Inclusion-Exclusion Principle."
Here it uses the fact that

#U = #(A u B) - #(A intersection B).

The lower case "u" denotes "union."

whenever you have any math related questions.

- Doctor Nitrogen, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Logic
High School Sets
Middle School Logic

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