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Thread: NOT version of the Inclusion-Exclusion principle

  1. August 20th 2011, 12:02 PM #1
    AkilMAI
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    NOT version of the Inclusion-Exclusion principle

    It may sound ridiculous but I can't find this anywhere on the web.
    Thanks in advance
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  2. August 20th 2011, 12:05 PM #2
    Plato
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    Re: NOT version of the Inclusion-Exclusion principle

    Quote Originally Posted by AkilMAI View Post
    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.
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  3. August 20th 2011, 12:48 PM #3
    AkilMAI
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    Re: NOT version of the Inclusion-Exclusion principle

    what is the NOT version of the Inclusion-Exclusion principle?
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  4. August 20th 2011, 12:58 PM #4
    Plato
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    Re: NOT version of the Inclusion-Exclusion principle

    Quote Originally Posted by AkilMAI View Post
    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"?
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  5. August 20th 2011, 01:06 PM #5
    AkilMAI
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    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
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  6. August 20th 2011, 01:22 PM #6
    Plato
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    Re: NOT version of the Inclusion-Exclusion principle

    Quote Originally Posted by AkilMAI View Post
    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.
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