Results 1 to 2 of 2

Math Help - Inclusion-Exclusion Principle Proof

  1. #1
    Junior Member
    Joined
    Sep 2010
    Posts
    36

    Inclusion-Exclusion Principle Proof

    Inductive Step
    Assume true for n so lA_1U.....UA_nl = lA_1l +....+ lA_nl - lA_1nA_2l +lA_1nA_2nA_3l -........+ (-1)^n-1lA_1n....nA_nl

    Now aim to prove true for n+1
    so we take finite sets A_1,.....,A_n,A_n+1

    lA_1U...UA_nUA_n+1l= lA_1U....UA_nl + lA_n+1l - l(A_1U....UA_n)nA_n+1l

    How do u use the inductive step to prove for n+1?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,615
    Thanks
    1578
    Awards
    1
    Quote Originally Posted by qwerty10 View Post
    Inductive Step
    Assume true for n so lA_1U.....UA_nl = lA_1l +....+ lA_nl - lA_1nA_2l +lA_1nA_2nA_3l -........+ (-1)^n-1lA_1n....nA_nl

    Now aim to prove true for n+1
    so we take finite sets A_1,.....,A_n,A_n+1

    lA_1U...UA_nUA_n+1l= lA_1U....UA_nl + lA_n+1l - l(A_1U....UA_n)nA_n+1l
    How do u use the inductive step to prove for n+1?
    The greatest drawback is notation. Here is one suggestion.
    \left| {A_1  \cup A_2  \cup  \cdots A_n } \right| = \sum\limits_j {\left| {A_j } \right|}  - \sum\limits_{j < k} {\left| {A_j  \cap A_k } \right|}  + \sum\limits_{j < k < n} {\left| {A_j  \cap A_k  \cap A_n } \right|}  \cdots ( - 1)^n \sum\limits_j {\left| {A_1  \cap A_2  \cap  \cdots A_n } \right|}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inclusion–exclusion principle
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 22nd 2011, 05:45 AM
  2. Inclusion Exclusion Principle Help!
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: September 28th 2011, 02:43 AM
  3. inclusion exclusion principle help!
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: August 9th 2011, 06:17 AM
  4. Inclusion - Exclusion Principle
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 15th 2011, 06:52 AM
  5. Principle of Inclusion of Exclusion
    Posted in the Statistics Forum
    Replies: 2
    Last Post: December 10th 2008, 12:15 PM

Search Tags


/mathhelpforum @mathhelpforum