# Thread: NOT version of the Inclusion-Exclusion principle

1. ## NOT version of the Inclusion-Exclusion principle

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

2. ## Re: NOT version of the Inclusion-Exclusion principle

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.

3. ## Re: NOT version of the Inclusion-Exclusion principle

what is the NOT version of the Inclusion-Exclusion principle?

4. ## Re: NOT version of the Inclusion-Exclusion principle

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"?

5. ## 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

6. ## Re: NOT version of the Inclusion-Exclusion principle

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.