# NOT version of the Inclusion-Exclusion principle

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• August 20th 2011, 12:02 PM
AkilMAI
NOT version of the Inclusion-Exclusion principle
It may sound ridiculous but I can't find this anywhere on the web.
Thanks in advance
• August 20th 2011, 12:05 PM
Plato
Re: NOT version of the Inclusion-Exclusion principle
Quote:

Originally Posted by AkilMAI
It may sound ridiculous but I can't find this anywhere on the web.

What is the question? That is a statement not a question.
• August 20th 2011, 12:48 PM
AkilMAI
Re: NOT version of the Inclusion-Exclusion principle
what is the NOT version of the Inclusion-Exclusion principle?
• August 20th 2011, 12:58 PM
Plato
Re: NOT version of the Inclusion-Exclusion principle
Quote:

Originally Posted by AkilMAI
what is the NOT version of the Inclusion-Exclusion principle?

Would take $\|A\|=\|A\cap B\|+\|A\cap \overline{B}\|$ were $\overline{B}$ is the complement of $B$ as example?

Or do you mean, "at its very root all counting is a version of the Inclusion-Exclusion principle"?
• August 20th 2011, 01:06 PM
AkilMAI
Re: NOT version of the Inclusion-Exclusion principle
I dont know how to answer. I have two exercisses from a book both say to define the NOT version of the Inclusion-Exclusion principle for three subsest A1,A2,A3 of a set A.The second exercise wants a formula for for the number of elements in A that don't belong in A1,A2,A3,A4.And I can't find it
• August 20th 2011, 01:22 PM
Plato
Re: NOT version of the Inclusion-Exclusion principle
Quote:

Originally Posted by AkilMAI
say to define the NOT version of the Inclusion-Exclusion principle for three subsest A1,A2,A3 of a set A.The second exercise wants a formula for for the number of elements in A that don't belong in A1,A2,A3,A4.And I can't find it

Say that $\mathcal{U}$ is a finite set and $A_k\subseteq\mathcal{U}$ for $k=1,2,3,4$.

Then $\|\mathcal{U}\|-\|\overline{A_1}\cap\overline{A_2}\cap\overline{A_ 3}\cap\overline{A_4}\|$ is the number of elements NOT in $A_1\cup A_2\cup A_3\cup A_4$

That is a guess as to what it may mean.